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Abstract Many codes have been developed to study highly relativistic, magnetized flows around and inside compact objects. Depending on the adopted formalism, some of these codes evolve the vector potential A , and others evolve the magnetic field B = ∇ × A directly. Given that these codes possess unique strengths, sometimes it is desirable to start a simulation using a code that evolves B and complete it using a code that evolves A. Thus transferring the data from one code to another would require an inverse curl algorithm. This paper describes two new inverse curl techniques in the context of Cartesian numerical grids: a cell-by-cell method, which scales approximately linearly with the numerical grid, and a global linear algebra approach, which has worse scaling properties but is generally more robust (e.g., in the context of a magnetic field possessing some nonzero divergence). We demonstrate these algorithms successfully generate smooth vector potential configurations in challenging special and general relativistic contexts. Highlights • Our solution consists of a numerical implementation of the "inverse curl" operator. • We use two different methods that have different strengths and weaknesses. • The cell-by-cell technique is very fast and scales with the number of gridpoints. • The global linear algebra method is slower but has better symmetry properties. [ABSTRACT FROM AUTHOR]

Abstract In cylindrical/spherical geometries, MHD solvers using explicit finite-volume methods face restrictive time steps imposed by the CFL condition due to the clustering of cells in the azimuthal direction near the pole/axis. We use a conservative averaging-reconstruction method (Ring Average) on structured cylindrical/spherical mesh to remove this severe time step restriction for multi-dimensional curvilinear finite-volume MHD solvers. The Ring Average technique is implemented as a post-processing step and thus requires no changes to the existing data structure, grid definition or numerical methods in the original MHD solver. This paper describes the Ring Average algorithm and presents simulation results using field loop advection and MHD blast waves in cylindrical/spherical geometries for validation. The algorithm is shown to be inexpensive and easily implemented in existing curvilinear finite-volume MHD solvers. Highlights • Ring Average is a "post-processing" module without modifying the original solver. • Ring Average relaxes time-step restrictions in MHD solvers with axis singularities. • Ring Average conserves mass, momentum and energy for proper shock propagations. • Ring Average works for codes with either divergence cleaning or constrained transport. [ABSTRACT FROM AUTHOR]

Centroidal Voronoi tessellation (CVT)-based mesh generation is a very effective technique for creating high-quality Voronoi meshes and their dual Delaunay triangulations that often play a crucial role in applications, including ocean and atmospheric simulations using finite volume schemes. In the next generation climate models, the spacing scales change dramatically across the whole sphere and require ultra-high resolution and smooth transitions from coarse to fine grid regions. Thus fast and robust spherical CVT (SCVT) meshing algorithms become highly desirable. In this paper, we first propose a Lloyd-preconditioned limited-memory BFGS method for constructing SCVTs that is also applicable to the construction of CVTs of general domains. This method is then parallelized based on overlapping domain decomposition, enabling excellent scalability on distributed systems. Results of several computational experiments show that the new method could incur computational time costs one order of magnitude smaller compared with some existing methods for generating large-scale highly variable-resolution meshes, while also providing significant improvements in mesh quality. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a development of the direction splitting algorithm for flows in complex geometries proposed in [2] to the case of flows containing rigid particles. The main novelty of this method is that the grid is fit to the time-dependent domain at each time step which allows for an optimal spatial approximation of the Navier–Stokes equations. In general, this is a very hard task for multidimensional problems. However, it is significantly simplified if the momentum equations are discretized by a direction splitting scheme. Such a scheme requires only solving a set of one-dimensional problems, and the grid can be easily fit to the boundary in the direction of each of these problems. Here we use a MAC discretization stencil but the same idea can be applied to other discretizations. The equations of motion of each particle are discretized explicitly and the computed particle velocities are imposed as Dirichlet boundary conditions for the Navier–Stokes equations on the adapted grid. The pressure is extended within the particles in a fictitious domain fashion, but the divergence stencil is fit to the particle boundaries. In this paper, the direction splitting algorithm with boundary fitting is compared to pure fictitious domain methods. [Copyright &y& Elsevier]

Proper orthogonal decomposition (POD) and its extension based on time-windows have been shown to greatly improve the effectiveness of recovering smooth ensemble solutions from noisy particle data. However, to successfully de-noise any molecular system, a large number of measurements still need to be provided. In order to achieve a better efficiency in processing time-dependent fields, we have combined POD with a well-established signal processing technique, wavelet-based thresholding. In this novel hybrid procedure, the wavelet filtering is applied within the POD domain and referred to as WAVinPOD. The algorithm exhibits promising results when applied to both synthetically generated signals and particle data. In this work, the simulations compare the performance of our new approach with standard POD or wavelet analysis in extracting smooth profiles from noisy velocity and density fields. Numerical examples include molecular dynamics and dissipative particle dynamics simulations of unsteady force- and shear-driven liquid flows, as well as phase separation phenomenon. Simulation results confirm that WAVinPOD preserves the dimensionality reduction obtained using POD, while improving its filtering properties through the sparse representation of data in wavelet basis. This paper shows that WAVinPOD outperforms the other estimators for both synthetically generated signals and particle-based measurements, achieving a higher signal-to-noise ratio from a smaller number of samples. The new filtering methodology offers significant computational savings, particularly for multi-scale applications seeking to couple continuum informations with atomistic models. It is the first time that a rigorous analysis has compared de-noising techniques for particle-based fluid simulations. [ABSTRACT FROM AUTHOR]

This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Simulation of charged-particle beam devices using particle-in-cell methods in (r, z) cylindrical coordinates can be extremely efficient, incorporating a majority of the physics and yielding high resolution with minimal computational costs. However, accuracy requires adjustment of solution coefficients and particle/current weights with radius, especially near the cylindrical axis. Prior algorithms have been based on special models and approximations with no consistent method for computing coefficients in general cases. The Local Taylor Polynomial (LTP) technique presented in this paper provides a general framework for determination of coefficients and development of PDE solution algorithms. The LTP method employs a local (polynomial) solution of the continuum PDE to construct numerical algorithms. As a result, LTP systematically generates accurate coefficients and incorporates fields and sources on an equal basis. This paper focuses on the scalar Poisson PDE in cylindrical coordinates to illustrate the LTP technique, coefficient derivation, electric field calculation and handling of space charge effects. Application of LTP to non-conformal boundaries and non-uniform grids is presented. Although focused on cylindrical coordinates in this paper, the LTP technique has general applicability to other PDE’s and geometries, and is broadly applicable to problems in beam/field simulation. [Copyright &y& Elsevier]

Abstract: This paper contributes to the state of the art in Cartesian-grid methods through development of new advection and reconstruction Volume-of-Fluid (VOF) algorithms which are applicable to two and three-dimensional flows. A computationally efficient and second-order VOF reconstruction method is presented which uses no inversions to determine the interface normal direction. Next, the lack of conservation of fluid volume in previous VOF advection methods are shown to be due to improper treatment of one-dimensional stretching in the velocity field. This paper uses simple explicit time stepping and a cell-center estimate of the volume fraction in the dilatation term to achieve a completely conservative advection method. The new methods are simple, robust and shown to out perform existing approaches for canonical test problems relevant to breaking wave flows. [Copyright &y& Elsevier]

A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale is proposed in this paper. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform, the Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are suggested. Using the algorithm, the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases discussed, the hybrid model is more than 10 times faster than just using the ESBI method, and it is also much faster than other methods reported in the literature. [ABSTRACT FROM AUTHOR]

This paper presents an in-depth analysis on the accuracy and performance of the windowed multipole Doppler broadening method. The basic theory behind cross section data is described, along with the basic multipole formalism followed by the approximations leading to windowed multipole method and the algorithm used to efficiently evaluate Doppler broadened cross sections. The method is tested by simulating the BEAVRS benchmark with a windowed multipole library composed of 70 nuclides. Accuracy of the method is demonstrated on a single assembly case where total neutron production rates and U 238 capture rates compare within 0.1% to ACE format files at the same temperature. With regards to performance, clock cycle counts and cache misses were measured for single temperature ACE table lookup and for windowed multipole. The windowed multipole method was found to require 39.6% more clock cycles to evaluate, translating to a 7.9% performance loss overall. However, the algorithm has significantly better last-level cache performance, with 3 fewer misses per evaluation, or a 65% reduction in last-level misses. This is due to the small memory footprint of the windowed multipole method and better memory access pattern of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. These scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation. [ABSTRACT FROM AUTHOR]

We propose a numerical framework which can simulate free surface flows with complex moving interfaces like droplet splashing as minimizing spurious currents. The numerical framework is based on the CLSVOF (coupled level set and volume-of-fluid) method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighted line interface calculation) scheme, multi-moment methods (CIP-CSL and VSIAM3) and density-scaled CSF (continuum surface force) model within a balanced force formulation. In this paper, we propose a level set based algorithm of the density-scaled balanced CSF model and show that the density-scaled balanced CSF model can reduce spurious currents more than the standard balanced CSF model without using the density-scaling when the exact curvature is not given. We also show that the numerical framework can well capture the physics of droplet splashing. [ABSTRACT FROM AUTHOR]

Abstract: There are a number of modeling challenges posed by space weather simulations. Most of them arise from the multiscale and multiphysics aspects of the problem. The multiple scales dramatically increase the requirements, in terms of computational resources, because of the need of performing large scale simulations with the proper small-scales resolution. Lately, several suggestions have been made to overcome this difficulty by using various refinement methods which consist in splitting the domain into regions of different resolutions separated by well defined interfaces. The multiphysics issues are generally treated in a similar way: interfaces separate the regions where different equations are solved. This paper presents an innovative approach based on the coexistence of several levels of description, which differ by their resolutions or, potentially, by their physics. Instead of interacting through interfaces, these levels are entirely simulated and are interlocked over the complete extension of the overlap area. This scheme has been applied to a parallelized, two-dimensional, Implicit Moment Method Particle in Cell code in order to investigate its multiscale description capabilities. Simulations of magnetic reconnection and plasma expansion in vacuum are presented and possible implementation options for this scheme on very large systems are also discussed. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the algorithmic improvement and careful analysis of the Fokker–Planck kinetic model derived by Jenny et al. [1] and Gorji et al. [2]. The motivation behind the Fokker–Planck based particle methods is to gain efficiency in low Knudsen rarefied gas flow simulations, where conventional direct simulation Monte Carlo (DSMC) becomes expensive. This can be achieved due to the fact that the resulting model equations are continuous stochastic differential equations in velocity space. Accordingly, the computational particles evolve along independent stochastic paths and thus no collision needs to be calculated. Therefore the computational cost of the solution algorithm becomes independent of the Knudsen number. In the present study, different computational improvements were persuaded in order to augment the method, including an accurate time integration scheme, local time stepping and noise reduction. For assessment of the performance, gas flow around a cylinder and lid driven cavity flow were studied. Convergence rates, accuracy and computational costs were compared with respect to DSMC for a range of Knudsen numbers (from hydrodynamic regime up to above one). In all the considered cases, the model together with the proposed scheme give rise to very efficient yet accurate solution algorithms. [Copyright &y& Elsevier]

Abstract: Parareal is a recent time parallelization algorithm based on a predictor–corrector mechanism. Recently, it has been applied for the first time to a fully-developed plasma turbulent simulation, and a qualitative understanding of how parareal converges exists for this case. In this paper, we construct an analytical framework of the process of convergence that should be applicable to parareal simulations of general turbulent systems. This framework allows one to gain a quantitative understanding of the dependence of the convergence on the physics of the problem and the choices that must be made to implement parareal. The analytical knowledge provided by this new framework can be used to optimize the implementation of parareal. We illustrate the inner workings of the framework and demonstrate its predictive capabilities by applying it to the modeling of the parareal convergence of drift-wave plasma turbulent simulations. [Copyright &y& Elsevier]

Abstract: Modern graphical processing units (GPUs) have recently become a pervasive technology able to rapidly solve large parallel problems which previously required runs on clusters or supercomputers. In this paper we propose an effective strategy to parallelize the T-matrix method on GPUs in order to speed-up light scattering simulations. We have tackled two of the most computationally intensive scattering problems that are of interest in nano-optics: the scattering from an isolated non-axisymmetric particle and from an agglomerate of arbitrary shaped particles. We show that fully exploiting the GPU potential we can achieve more than 20 times (20×) acceleration over sequential execution in the investigated scenarios, opening exciting prospectives in the analysis and the design of optical nanostructures. [Copyright &y& Elsevier]

Abstract: This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or continuum solvers in different parts of computational domains. We first review the discrete velocity method for solving Boltzmann and Wang Chang–Uhlenbeck kinetic equations for rarefied gases. Then, peculiarities of AMR implementation with octree Cartesian mesh are discussed. A Unified Flow Solver (UFS) uses AMAR method with adaptive Cartesian mesh to dynamically introduce kinetic patches for multi-scale simulations of gas flows. We describe fluid plasma models with AMR capabilities and illustrate how physical models affect simulation results for gas discharges, especially in the areas where electron kinetics plays an important role. We introduce Eulerian solvers for plasma kinetic equations and illustrate the concept of adaptive mesh in velocity space. Specifics of electron kinetics in collisional plasmas are described focusing on deterministic methods of solving kinetic equations for electrons under different conditions. We illustrate the appearance of distinct groups of electrons in the cathode region of DC discharges and discuss the physical models appropriate for each group. These kinetic models are currently being incorporated into AMAR methodology for multi-scale plasma simulations. [Copyright &y& Elsevier]

Abstract: This is the first of two papers devoted to the analysis of contour crossing errors that occur in contour-advective simulations of fluid motion. Here an algorithm is presented for quantifying the error due to contour crossings. The first step is to determine the relative proximity of all possible pairs of contours. A digital representation of each contour is produced to aid in the corresponding calculation. Simple analysis of functions is then used to find any crossings between contours deemed close to each other by the digital representation method. Next, the area in error of a pair of crossing contours is calculated by identifying the polygon or polygons that approximately bound the erroneous region. Finally, some preliminary results of analysis of contour crossings that occur in contour-advective semi-lagrangian (CASL) simulations of single layer quasigeostrophic turbulence are presented. It is shown that the error due to contour crossings is small in the simulations considered here. [Copyright &y& Elsevier]

Abstract: This is the second of two papers devoted to the analysis of contour crossing errors that occur in contour-advective simulations of fluid motion, where either vorticity or potential vorticity is represented by contours. We begin with a detailed discussion on some of the potential mechanisms for contour crossing. Past work has suggested that the formation of contour crossings is due to inadequate spatial resolution of contours . The implementation of two schemes for preventing contour crossings within the framework of the Contour-Advective Semi-Lagrangian (CASL) algorithm is detailed here. We then present an analysis of contour crossing errors in simulations of quasigeostrophic turbulence on the f-plane and the quasigeostrophic motion of an initially circular vortex patch on the β-plane using the algorithm detailed in Part 1. We find that in general individual crossings occur at scales smaller than the inversion grid scale on which velocity is calculated, but at scales larger than that of the surgical scale that defines the smallest resolved features (vorticity) of a flow. If the resolution of a quasigeostrophic turbulence simulation on the f-plane is increased by doubling the number of grid points in each coordinate direction used in the calculation of the velocity field, then the total area in error due to contour crossings remains unchanged; a smaller number of crossings introducing larger scale area errors is replaced by a greater number of smaller local errors. Uniformly increasing the density of nodes along all contours and placement of nodes at points of close approach on contours are both effective methods for limiting contour crossings. [Copyright &y& Elsevier]

Abstract: This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov–Poisson formulation), ours is based on a nonlinearly converged Vlasov–Ampére (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant–Friedrichs–Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicit time steps (unlike the earlier “energy-conserving” explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton–Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible. [Copyright &y& Elsevier]

Abstract: The paper introduces a high-order, adaptive finite-element method for simulation of sonic measurements acquired with borehole-eccentered logging instruments. The resulting frequency-domain based algorithm combines a Fourier series expansion in one spatial dimension with a two-dimensional high-order adaptive finite-element method (FEM), and incorporates a perfectly matched layer (PML) for truncation of the computational domain. The simulation method was verified for various model problems, including a comparison to a semi-analytical solution developed specifically for this purpose. Numerical results indicate that for a wireline sonic tool operating in a fast formation, the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole (eccentricity distance). However, new flexural modes arise with an increase in eccentricity distance. In soft formations, we identify a new dipole tool mode which arises as a result of tool eccentricity. [Copyright &y& Elsevier]

Abstract: Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend the study of Veerapaneni et al. [S.K. Veerapaneni, D. Gueyffier, G. Biros, D. Zorin, A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows, Journal of Computational Physics 228 (19) (2009) 7233–7249] to general non-axisymmetric vesicle flows in three dimensions. Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is needed to ensure stability of the time-stepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere. By introducing these algorithmic components, we obtain a time-stepping scheme that circumvents the stability constraint on the time-step and achieves spectral accuracy in space. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows. [Copyright &y& Elsevier]

Abstract: This paper presents an output-based adaptive algorithm for unsteady simulations of convection-dominated flows. A space–time discontinuous Galerkin discretization is used in which the spatial meshes remain static in both position and resolution, and in which all elements advance by the same time step. Error estimates are computed using an adjoint-weighted residual, where the discrete adjoint is computed on a finer space obtained by order enrichment of the primal space. An iterative method based on an approximate factorization is used to solve both the forward and adjoint problems. The output error estimate drives a fixed-growth adaptive strategy that employs hanging-node refinement in the spatial domain and slab bisection in the temporal domain. Detection of space–time anisotropy in the localization of the output error is found to be important for efficiency of the adaptive algorithm, and two anisotropy measures are presented: one based on inter-element solution jumps, and one based on projection of the adjoint. Adaptive results are shown for several two-dimensional convection-dominated flows, including the compressible Navier–Stokes equations. For sufficiently-low accuracy levels, output-based adaptation is shown to be advantageous in terms of degrees of freedom when compared to uniform refinement and to adaptive indicators based on approximation error and the unweighted residual. Time integral quantities are used for the outputs of interest, but entire time histories of the integrands are also compared and found to converge rapidly under the proposed scheme. In addition, the final output-adapted space–time meshes are shown to be relatively insensitive to the starting mesh. [Copyright &y& Elsevier]

Abstract: A stencil adaptive lattice Boltzmann method (LBM) is developed in this paper. It incorporates the stencil adaptive algorithm developed by Ding and Shu for the solution of Navier–Stokes (N–S) equations into the LBM calculation. Based on the uniform mesh, the stencil adaptive algorithm refines the mesh by two types of 5-points symmetric stencils, which are used in an alternating sequence for increased refinement levels. The two types of symmetric stencils can be easily combined to form a 9-points symmetric structure. Using the one-dimensional second-order interpolation recently developed by Wu and Shu along the straight line and the D2Q9 model, the adaptive LBM calculation can be effectively carried out. Note that the interpolation coefficients are only related to the lattice velocity and stencil size. Hence, the simplicity of LBM is not broken down and the accuracy is maintained. Due to the use of adaptive technique, much less mesh points are required in the simulation as compared to the standard LBM. As a consequence, the computational efficiency is greatly enhanced. The numerical simulation of two dimensional lid-driven cavity flows is carried out. Accurate results and improved efficiency are reached. In addition, the steady and unsteady flows over a circular cylinder are simulated to demonstrate the capability of proposed method for handling problems with curved boundaries. The obtained results compare well with data in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Several plasma devices, including Hall and ion thrusters, operate by ionizing a low density neutral gas for which the mean free path between collisions of gas molecules is greater than typical device dimensions. In general, the discrete-particle algorithms used to calculate the neutral gas ignore velocity changes due to collisions between gas molecules. However, particle algorithms are a source of unphysical statistical noise that may detract from the study of the plasma physics, the prime purpose of most simulations. In this paper we present a new neutral gas algorithm for use in plasma simulation codes that exploits the fact that very few collisions change the velocity of neutral gas molecules. The algorithm assumes that the particle velocity distribution function for neutrals emitted from a given surface remains unchanged except for a scale factor that reflects the loss of neutrals to ionization. The sources of neutrals may be gas inlets, and isotropic, thermally accommodated, gas molecules coming off chamber surfaces including recombined ions. The algorithm is implemented in two dimensions (R–Z) with emitting surfaces represented as surfaces of revolution. The advantage of this algorithm over the conventional particle approach is the absence of statistical noise. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, three improvements for modelling surface tension-dominated interfacial flows using interface tracking-based solution algorithms are presented. We have developed an improved approach to curvature estimation for incorporation into modern mesh-based surface tension models such as the Continuum Surface Force (CSF) and Sharp Surface Force (SSF) models. The scheme involves generating samples of curvature estimates from the multitude of height functions that can be generated from VOF representations of interfaces, and applying quality statistics based on interface orientation and smoothness to choose optimal candidates from the samples. In this manner, the orientation-dependence of past schemes for height function-based curvature estimation is ameliorated, the use of compact stencils for efficient computation can be maintained, and robustness is enhanced even in the presence of noticeable subgrid-scale disturbances in the interface representation. For surface tension-dominated flows, the explicit capillary timestep restriction is relaxed through timescale-separated slope limiting that identifies spurious modes in curvature evolution and omits them from contributing to surface force computations, thus promoting efficiency in simulation through the use of less timesteps. Efficiency in flow simulation is further promoted by incorporating awareness of interface location into multigrid preconditioning for Krylov subspace-based solution of elliptic problems. This use of interface-cognizance in solving problems such as the Helmholtz equation and the Poisson equation enables multigrid-like convergence in discontinuous-coefficient elliptic problems without the expense of constructing the Galerkin coarse-grid operator. The key improvements in the surface tension modelling and the numerical linear algebra are also applicable to level-set-based interfacial flow simulation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation. [Copyright &y& Elsevier]

Abstract: The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples. [Copyright &y& Elsevier]

Abstract: In this paper, a stochastic model is presented to simulate the flow of gases, which are not in thermodynamic equilibrium, like in rarefied or micro situations. For the interaction of a particle with others, statistical moments of the local ensemble have to be evaluated, but unlike in molecular dynamics simulations or DSMC, no collisions between computational particles are considered. In addition, a novel integration technique allows for time steps independent of the stochastic time scale. The stochastic model represents a Fokker–Planck equation in the kinetic description, which can be viewed as an approximation to the Boltzmann equation. This allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations. The fluid dynamic equations of Navier–Stokes and Fourier are fully recovered for small relaxation times, while for larger values the new model extents into the kinetic regime. Numerical studies demonstrate that the stochastic model is consistent with Navier–Stokes in that limit, but also that the results become significantly different, if the conditions for equilibrium are invalid. The application to the Knudsen paradox demonstrates the correctness and relevance of this development, and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages. Moreover, results of a test case with geometrically complex boundaries are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we develop the discrete compatibility-constraint pressure-correction algorithm for transient simulations of variable density flows at low-Mach numbers. The constraint for the velocity field is constructed from a combination of the discrete equations of continuity and scalar (e.g. energy) transport, imposing that the newly predicted state must be compatible, in agreement with the equation of state. This way, mass and scalar conservation are guaranteed and the equation of state is exactly fulfilled at every time step. For comparison reasons, two other types of well-known pressure-correction algorithms are also used. The first class, denoted as continuity-constraint pressure-correction, is based on a constraint for the velocity field that is derived solely from the continuity equation. The second class, denoted as analytical compatibility-constraint pressure-correction, constructs the constraint from an analytical combination of the material derivative of the equation of state and the continuity and scalar equations. The algorithms are tested for three example fluid configurations: a single-fluid ideal gas, a two-fluid inert mixture and a two-fluid reacting mixture. The latter is special in the sense that the equation of state is non-linear and not everywhere differentiable. The continuity-constraint pressure-correction algorithm yields unstable solutions if density ratios are high. The analytical compatibility-constraint pressure-correction algorithm yields stable results, but the predicted states do not correspond to the equation of state. The discrete compatibility-constraint pressure-correction algorithm performs well on all test cases: the simulation results are stable and exactly match the equation of state. [Copyright &y& Elsevier]

Abstract: Edge detection has traditionally been associated with detecting physical space jump discontinuities in one dimension, e.g. seismic signals, and two dimensions, e.g. digital images. Hence most of the research on edge detection algorithms is restricted to these contexts. High dimension edge detection can be of significant importance, however. For instance, stochastic variants of classical differential equations not only have variables in space/time dimensions, but additional dimensions are often introduced to the problem by the nature of the random inputs. The stochastic solutions to such problems sometimes contain discontinuities in the corresponding random space and a prior knowledge of jump locations can be very helpful in increasing the accuracy of the final solution. Traditional edge detection methods typically require uniform grid point distribution. They also often involve the computation of gradients and/or Laplacians, which can become very complicated to compute as the number of dimensions increases. The polynomial annihilation edge detection method, on the other hand, is more flexible in terms of its geometric specifications and is furthermore relatively easy to apply. This paper discusses the numerical implementation of the polynomial annihilation edge detection method to high dimensional functions that arise when solving stochastic partial differential equations. [Copyright &y& Elsevier]

Abstract: The three-dimensional, moving mesh interface tracking (MMIT) method coupled with local mesh adaptations by Quan and Schmidt [S.P. Quan, D.P. Schmidt, A moving mesh interface tracking method for 3D incompressible two-phase flows, J. Comput. Phys. 221 (2007) 761–780] demonstrated the capability to accurately simulate multiphase flows, to handle large deformation, and also to perform interface pinch-off for some specific cases. However, another challenge, i.e. how to handle interface merging (such as droplet coalescence) has not been addressed. In this paper, we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup. These two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region. After the conversion, the newly created interface is usually ragged, and a local projection method is employed to smooth the interface. Extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes. Simulations of droplet pair collisions including both head-on and off-center coalescences show that the mesh adaptations are capable of resolving very small length scales, and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows. The potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed. [Copyright &y& Elsevier]

Abstract: In this paper, a pressure-based semi-implicit algorithm for compressible flows is described. This type of solver is of great interest in combustion devices where the flow speed is small but where the unsteady heat release can be coupled to the acoustic modes and lead to instabilities. The fractional-step method used in this algorithm is based on a characteristic splitting, which clearly separates the acoustics from the advection. This splitting allows to use adapted numerics for these different time-scales. The algorithm is second-order in space and time for linear acoustics and for low-Mach advection without iterating the time-step. Moreover, when kinetic-energy conserving schemes are used for the predictor step, the algorithm discretely conserves the kinetic energy in the low-Mach limit. All these properties are illustrated on simple test cases and the algorithm is finally validated by performing the LES of the cold flow of an industrial burner. [Copyright &y& Elsevier]

Abstract: Particle simulations in fields ranging from biochemistry to astrophysics require the evaluation of interactions between all pairs of particles separated by less than some fixed interaction radius. The applicability of such simulations is often limited by the time required for calculation, but the use of massive parallelism to accelerate these computations is typically limited by inter-processor communication requirements. Recently, Snir [M. Snir, A note on N-body computations with cutoffs, Theor. Comput. Syst. 37 (2004) 295–318] and Shaw [D.E. Shaw, A fast, scalable method for the parallel evaluation of distance-limited pairwise particle interactions, J. Comput. Chem. 26 (2005) 1318–1328] independently introduced two distinct methods that offer asymptotic reductions in the amount of data transferred between processors. In the present paper, we show that these schemes represent special cases of a more general class of methods, and introduce several new algorithms in this class that offer practical advantages over all previously described methods for a wide range of problem parameters. We also show that several of these algorithms approach an approximate lower bound on inter-processor data transfer. [Copyright &y& Elsevier]

In this paper we present a self-consistent simulation model of colliding beams in high energy ring colliders. The model, which is based on a particle-in-cell method, uses a new developed shifted effective Green function algorithm for the efficient calculation of the beam–beam interaction with arbitrary separation and large aspect ratio. The model uses transfer maps to treat the external focusing elements and a stochastic map to treat radiation damping and quantum excitation of the beams. In the parallel implementation we studied various strategies to deal with the particular nature of the colliding beam system – a system in which there can be significant particle movement between beam–beam collisions. We chose a particle-field decomposition approach instead of the conventional domain decomposition or particle decomposition approach. The particle-field approach leads to good load balance, reduced communication cost, and shows the best scalability on an IBM SP3 among the three parallel implementations we studied. A performance test of the beam–beam model on a Cray T3E, IBM SP3, and a PC cluster is presented. As an application, we studied the flip–flop instability in an electron–positron collider. [Copyright &y& Elsevier]