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For the evaluation of charge carrier transport in quantum devices, quantum Liouville-type equations (QLTE) have proven to be powerful as a starting point for the numerical analysis of transport characteristics. Due to the complexity of quantum devices, the computational time is to be further reduced using high-performance computing methods. Therefore, a hybrid discontinuous Galerkin (DG) approach is proposed to solve quantum Liouville-type equations (QLTE) efficiently. Due to resulting block diagonal matrices occurring after an approximation, the system matrix can be computed efficiently without an inversion of large matrices when considering time-dependent analyses. As a result, the time-dependent exponential integrator can be represented as a polynomial of the resulting system matrix and the time evolution can be explicitly determined via matrix-vector multiplications. Most importantly, along with the discontinuous Galerkin approach, the accuracy via an appropriate choice of elements can be improved. The general approach is presented and validated. [ABSTRACT FROM AUTHOR]

As the finite element method (FEM) and the finite volume method (FVM), both their traditional and high-order variants, continue their proliferation into various applied engineering disciplines, adaptive mesh refinement and optimization strategies have increased in their importance when solving real-world computational fluid mechanics applications. The post-processing and visualization of the resulting flow fields present two significant analysis and visualization challenges. The first challenge is the handling of elemental continuity, which is often only C 0 continuous (in continuous Galerkin methods) or piecewise discontinuous (in discontinuous Galerkin methods). The second challenge is that, depending on the flow regime and the geometric configurations for which adaptive meshing strategies are used, the meshes generated are often highly anisotropic. The (uniform knot) line-SIAC (L-SIAC) filter has been proposed as a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous. In this paper, we demonstrate that the state-of-the-art adaptive L-SIAC filter, designed for mildly anisotropic meshes, suffers degradation in the quality of the post-processed solution when applied to the types of highly anisotropic meshes produced through adaptive mesh refinement and optimization. Hence, a new Non-Uniform Knot (NUK) L-SIAC filter is proposed that automatically conforms to the underlying mesh anisotropy. We demonstrate that the new filter behaves similarly to the adaptive L-SIAC filter when applied to uniform and mildly anisotropic meshes, and furthermore we show the superiority of the NUK L-SIAC filter when applied to highly anisotropic meshes. The newly formulated filter is applied to 2D canonical scalar fields and used to visualize 2D and 3D fluid flow simulation results. • This study analyzes and visualizes principle and derived fields from FEM and FVM methods used over highly anisotropic meshes with element length ratios of up to 1000:1. • A new Non-Uniform Knot (NUK) L-SIAC filter is proposed to address issues with the adaptive L-SIAC filter on highly anisotropic meshes. • The NUK L-SIAC filter performs similarly to the adaptive L-SIAC filter on uniform and mildly anisotropic meshes but outperforms it on highly anisotropic meshes. [ABSTRACT FROM AUTHOR]

High order entropy stable schemes provide improved robustness for computational simulations of fluid flows. However, additional stabilization and positivity preserving limiting can still be required for variable-density flows with under-resolved features. We demonstrate numerically that entropy stable Discontinuous Galerkin (DG) methods which incorporate an “entropy projection” are less likely to require additional limiting to retain positivity for certain types of flows. We conclude by investigating potential explanations for this observed improvement in robustness.

In this article, a nonconformal and nonoverlapping domain decomposition method (DDM) based on surface integral equation (SIE) is proposed for the electromagnetic (EM) scattering or radiation of multiscale metallic targets. To reduce the unknown amount of the conventional SIE for multiscale EM simulation, we apply curved triangular elements and higher order hierarchical vector (HOHV) basis functions to the SIE. Next, to increase the flexibility of geometrical modeling and accelerate the convergence of the presented SIE system for electrically large and multiscale metallic targets, a DDM scheme is further developed to employ a discontinuous Galerkin (DG) approach to glue conformal/nonconformal surface grids between adjacent subdomains. In addition, an interior penalty term is introduced to stabilize the DDM solution, and half edge-based HOHV basis functions are introduced to model the current associated with nonconformal surface elements. Meanwhile, the basis expansion and recombination (BER) technique is introduced to significantly accelerate the matrix-filling and improve the efficiency. The flexibility of basis order selection is further enhanced by the hierarchical characteristic of HOHV bases. Finally, several numerical results are provided to demonstrate the accuracy, efficiency, and flexibility of the proposed HO-DG-DDM. [ABSTRACT FROM AUTHOR]

In this communication, we present flexible and efficient solutions of large-scale electromagnetic scattering problems using the parallel discontinuous Galerkin (DG) surface integral equation (SIE) method. A simplified formulation of the conventional DG is used by removing the interior penalty term, thereby avoiding computational burden of the contour integral in the conventional DG. It is demonstrated numerically that the simplification causes convergence deficiency and changes the accuracy convergence rate of the solution for objects with sharp corners. The former is overcome by constructing preconditioners using the near-field matrix of the whole region, and the latter is proved to have a neglectable influence on the accuracy of the final solutions as long as normal mesh density requirement is satisfied. The wellscaling ternary parallelization approach of the multilevel fast multipole algorithm (MLFMA) is incorporated into the DG domain decomposition framework to reduce the complexity of the solution and strength its capability for large-scale problems, with the distribution of the nearfield-related calculation adjusted to adapt the nonuniform meshes for a better workload balance. Numerical results are included to validate the accuracy and demonstrate the scalability and versatility of the proposed method. In addition, we demonstrated the effectiveness of our algorithm by solving a high-definition complicated aircraft model with inlets and exhausts involving over one billion unknowns. [ABSTRACT FROM AUTHOR]

A generalized transition matrix (GTM) model combined with discontinuous Galerkin (DG) method is proposed to analyze the scattering problems of open-ended cavities. A virtual reference surface is put to seal the opening of an open cavity and can separate it into an exterior region and an interior region. By mapping the scattering properties of the internal components onto the reference surface, the information interaction of the GTM model occurs on the reference surface only. With its features of nonconformal meshes at the boundary, the DG method makes the model feasible and accurate regardless of the normal continuity of the surface current at the transitional interface. The GTM model is independent of the exterior structure of the cavity and the external fields. The computational cost can be significantly decreased when the GTM model with the identical inner region is reused. Numerical examples demonstrate good precision and efficiency of the presented method.

We present a node-based discontinuous Galerkin (DG) pseudospectral time domain (PSTD) algorithm, with adaptive nonconformal unstructured meshes, for 3-D large-scale Maxwell’s equations. This algorithm is a combination of a new DG algorithm and a PSTD method, where spectral accuracy is achieved via the PSTD algorithm, while the DG serves as a stable coupling for multiple domains with unstructured hexahedra. Time marching is efficient because the mass matrix in the DG-PSTD algorithm is exactly diagonal. The scheme is low-storage and scalable because the stiffness matrix is localized into a small shared matrix. Furthermore, arbitrary nonconformal meshes can be adaptively realized, increasing the flexibility of complex media modeling. Our numerical results corroborate the long-time stability, high efficiency, and high-order accuracy of the proposed solver. Finally, an adaptive application of 5G electromagnetic signal propagation demonstrates the efficiency and capability of the proposed high-order solver. [ABSTRACT FROM AUTHOR]

A nonconformal and nonoverlapping domain decomposition method (DDM) based on hybrid volume and surface integral equation (VSIE) is presented for modeling complex thin dielectric/perfect electric conductor (PEC) composite targets. To reduce the unknown amount of the conventional volume integral equation (VIE) for thin dielectric bulks, the improved simplified prism vector (ISPV) basis function is developed. By using the basis function, the volume integrals can be simplified into surface integrals or line integrals, which significantly reduce the simulation time. Prism grids can also avoid the overmeshing problem for thin dielectrics. Moreover, they can be perfectly matched to the triangular meshes widely used in surface integral equation (SIE) hence assures a simple and robust VSIE implementation. Next, in order to increase the flexibility of geometrical modeling and accelerate the convergence of the presented VSIE system for electrically large and multiscale composite targets, a DDM is further developed. In this DDM scheme, discontinuous Galerkin approaches are, respectively, employed for VIE and SIE, accounting for conformal/nonconformal volume grids and surface grids between adjacent subdomains. In addition, an interior penalty term is introduced to stabilize the DDM solution. Finally, some numerical results are considered and analyzed to show the validity, efficiency, and applicability of the presented scheme. [ABSTRACT FROM AUTHOR]

An hp- and memory-adaptive discontinuous Galerkin time-domain algorithm is presented to efficiently model wave propagation in poroelastic media, with the incorporation of 3-D fully anisotropic intrinsic attenuation. From the perspective of physics, the attenuation from the triclinic rock frame, the loss in the pore fluid, and the friction for their interaction are all considered. From the perspective of implementation, a new frequency-domain constitutive equation is introduced, involving complex-valued poroelasticity matrix. A new Q value is defined as the ratio between its real and imaginary parts for every entry. Then, a generalized Maxwell body is adopted to approximate this frequency-dependent Q in the time domain. Mathematically speaking, the hyperbolicity is preserved for the new viscous poroelastic system. Our results corroborate that the intrinsic attenuation anisotropy makes tangible effects in fluid-saturated porous formations. [ABSTRACT FROM AUTHOR]

This work describes the development of a hybrid framework of Runge–Kutta (RK), discontinuous Galerkin (DG), level set (LS) and direct ghost fluid (DGFM) methods for the simulation of near-field and early-time underwater explosions (UNDEX) in early-stage ship design. UNDEX problems provide a series of challenging issues to be solved. The multi-dimensional, multi-phase, compressible and inviscid fluid-governing equations must be solved numerically. The shock front in the solution field must be captured accurately while maintaining the total variation diminishing (TVD) properties. The interface between the explosive gas and water must be tracked without letting the numerical diffusion across the material interface lead to spurious pressure oscillations and thus the failure of the simulation. The non-reflecting boundary condition (NRBC) must effectively absorb the wave and prevent it from reflecting back into the fluid. Furthermore, the CFD solver must have the capability of dealing with fluid–structure interactions (FSI) where both the fluid and structural domains respond with significant deformation. These issues necessitate a hybrid model. In-house CFD solvers (UNDEXVT) are developed to test the applicability of this framework. In this development, code verification and validation are performed. Different methods of implementing non-reflecting boundary conditions (NRBCs) are compared. The simulation results of single and multi-dimensional cases that possess near-field and early-time UNDEX features—such as shock and rarefaction waves in the fluid, the explosion bubble, and the variation of its radius over time—are presented. Continuing research on two-way coupled FSI with large deformation is introduced, and together with a more complete description of the direct ghost fluid method (DGFM) in this framework will be described in subsequent papers.

The cell method (CM) or discrete geometric approach (DGA) in the time domain, already introduced by Codecasa et al. in 2008 for the coupled Ampere–Maxwell and Faraday equations, is here recast as a Galerkin Method similar to the finite-element method (FEM). In particular, it is shown to be a mixed method comprising an explicit scheme and two discontinuous Galerkin (DG) FEM spaces formulated on dual meshes, in which each of the two function spaces provides a continuous numerical flux choice for its dual mesh counterpart. The implemented version is shown to compare favorably in terms of accuracy and efficiency with respect to the classic conforming FEM scheme using Whitney elements. When tested on the same tetrahedral mesh, the Courant–Friedrichs–Lewy (CFL) condition for the proposed approach is a factor of 2 less restrictive on the time step with respect to the curl-conforming FEM scheme. [ABSTRACT FROM AUTHOR]

A time-domain discontinuous Galerkin Poggio–Miller–Chang–Harrington–Wu integral equation method, which is based on marching-on-in-degree (MOD) scheme, is proposed to simulate electromagnetic pulse (EMP) responses of arbitrarily shaped dielectric objects, where half Rao–Wilton–Glisson basis functions are chosen as the spatial basis ones. Both electric and magnetic current continuities between adjacent elements are guaranteed by introducing additional interior penalty terms. Therefore, three-dimensional dielectric structures with either conformal or nonconformal meshes can be treated. Meanwhile, the weighted Laguerre polynomials are chosen as the temporal basis functions and implemented for the MOD scheme, and stable EMP responses can be captured. Since our method is based on the surface integral equation with the objects’ surface meshed, the number of unknowns are significantly reduced in comparison with that of the volume integral equation method. Some numerical examples are presented to validate both stability and accuracy of the developed algorithm. [ABSTRACT FROM AUTHOR]

Visualizing high-order finite element simulation data using current visualization tools has many challenges: discontinuities at element boundaries, interpolating artifacts, and evaluating derived quantities. These challenges have been addressed by postprocessing the simulation data using the L-SIAC filter. However, the time required to postprocess using this filter needs to be addressed to enable using it on large datasets. In this work, we introduce an efficient technique to speed-up the L-SIAC filter and alternate ways to gain further speed-up at the cost of accuracy. This method is also ideal to postprocess at regularly spaced locations, which would be suitable for standard visualization software. Our results show that our method can achieve up to two orders of magnitude speed-up as compared to our interpretation of the technique presented in Docampo-Sánchez (SIAM J Sci Comput 39(5):A2179–A2200, 2017). [ABSTRACT FROM AUTHOR]

A sparse grid stochastic collocation method combined with discontinuous Galerkin method is developed for solving convection dominated diffusion optimal control problem with random coefficients. By the optimal control theory, an optimality system is obtained for the problem, which consists of a state equation, a co-state equation and an inequality. Based on finite dimensional noise assumption of random field, the random coefficients are assumed to have finite term expansions depending on a finite number of mutually independent random variables in the probability space. An approximation scheme is established by using a discontinuous Galerkin method for the physical space and a sparse grid stochastic collocation method based on the Smolyak construction for the probability space, which leads to the solution of uncoupled deterministic problems. A priori error estimates are derived for the state, co-state and control variables. Numerical experiments are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a method for the treatment of multiply connected regions within the semi-explicit time-domain discontinuous Galerkin (DG) eddy current solver based on the ${H}$ – $\Phi $ field formulation. The suggested method utilizes a multivalued magnetic scalar potential over a cutting surface that divides a multiply connected domain into two simply connected regions. The multivalued magnetic scalar potential in the nonconductive domain ($\Phi $ -domain) is regularly updated after a sequence of time steps of the explicit vector DG-finite element method solver in the electrically conductive domain (${H}$ -domain) yielding an accurate time-domain solution of the magnetic field in the multiply connected space surrounding the eddy current region. The efficiency and accuracy of the method are demonstrated by a 3-D example and the obtained results are verified by comparison against the corresponding frequency-domain solution. [ABSTRACT FROM AUTHOR]

A high-order discontinuous Galerkin (DG) method with nonconformal meshes is developed to accurately simulate large-scale poroelastic wave propagation in 3-D isotropic media. An exact upwind flux is succinctly derived to serve as an accurate coupling solver for the DG algorithm. Specifically, the eigenvalue problem in the Riemann solution is effectively reduced from the rank of 13 to 4. Furthermore, this new numerical flux gives more explicit physical insight, which indicates three-type waves in poroelastic media: two P waves and one S wave. Validations and verifications with analytical/semianalytical numerical solutions demonstrate the accuracy, robustness, and flexibility of the proposed solver. [ABSTRACT FROM AUTHOR]

A discontinuous Galerkin time-domain electric field integral equation method based on a marching-on-in-degree (MOD) scheme for simulating transient responses of perfect electric conductor objects is proposed in this letter. With the help of half-Rao–Wilton–Glisson spatial basis functions, we can simulate transient scattering responses of three-dimensional structures with either conformal or nonconformal meshes. The weighted Laguerre polynomials are chosen as temporal basis functions and implemented for the MOD scheme. Under such circumstances, the developed algorithm eliminates late-time instabilities and the limitation of Courant–Friedrichs–Lewy criteria. In addition, we adopt a fast-Fourier-transform-based blocking scheme to accelerate the temporal convolution of the MOD procedure. Some numerical examples are given to validate its stability and accuracy. [ABSTRACT FROM AUTHOR]

A rigorous stability analysis of the previously published semi-explicit time domain discontinuous Galerkin (DG) H– $\Phi $ approach for eddy current simulations is presented. The considered DG finite-element method (FEM) enables explicit time stepping in electrically conducting regions and eliminates the need for solving large sparse ill-conditioned equation systems. The considered method utilizes the magnetic scalar potential in electrically non-conducting regions computed by using the nodal finite elements. The theoretical stability limit of the considered semi-explicit time domain approach is obtained by applying the z-transform on the discrete time domain DG-FEM equations and by performing an eigenvalue analysis of the underlying elemental DG-FEM matrices. The obtained results are tested on simple 3-D examples, and an excellent agreement between the theoretical stability limit and the empirically obtained values was found. [ABSTRACT FROM AUTHOR]

We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave propagation in viscous media. To include the attenuation and dispersion due to the quality factor in time domain, several sets of auxiliary ordinary differential equations (AODEs) are added. Unlike the conventional auxiliary partial differential equation-based algorithm, this new method is highly parallel with its lossless counterpart, thus requiring much less time and storage consumption. Another superior property of the AODE-based DG method is that a novel exact Riemann solver can be derived, which allows heterogeneous viscoelastic coupling, in addition to accurate coupling with purely elastic media and fluid. Furthermore, thanks to the nonconformal-mesh technique, adaptive hp-refinement and flexible memory allocation for the auxiliary variables are achieved. Numerical results demonstrate the efficiency and accuracy of our method. [ABSTRACT FROM PUBLISHER]

A discontinuous Galerkin (DG) augmented electric field integral equation method based on the domain decomposition is proposed in this paper for full-wave solution of multiscale targets. The conventional surface integral equation-based DG method allowing both conformal and nonconformal discretizations for multiscale structures suffers from low-frequency breakdown. By augmenting the DG-EFIE with current continuity equation, the proposed scheme can alleviate the low-frequency breakdown. In the augmented system, the electric field integral equation and the current continuity equation are discretized by using hybrid basis functions including Rao–Wilton–Glisson (RWG) and half RWG basis functions. Since the half RWG basis is not divergence conforming, line charge degrees of freedom on the adjoining edges are introduced in this paper. It is observed that the resulting linear system is well conditioned at low frequencies, which leads to a rapid convergence over wide frequency band. Numerical examples demonstrate the accuracy and efficiency of the augmented system. [ABSTRACT FROM AUTHOR]

A semi-explicit time domain method for solving eddy current problems is presented. The suggested method is based on the discontinuous Galerkin (DG) finite-element approach and the H- $\Phi $ formulation of eddy current problem. The DG-technique allows for explicit time stepping in electrically conducting domains without solving a large sparse ill-conditioned linear equations system. The H- $\Phi $ field formulation enables the use of the magnetic scalar potential in electrically non-conducting domains that are discretized by using nodal finite elements. The application of the method is demonstrated by a 3-D example and the obtained results are verified by comparison with the corresponding frequency domain solution. [ABSTRACT FROM AUTHOR]

We present a discontinuous Galerkin pseudospectral time-domain (DG-PSTD) algorithm to solve elastic-/acoustic-wave propagation problems. The developed DG-PSTD algorithm combines the merits of flexibility from a finite-element method and spectral accuracy and efficiency from a high-order pseudospectral method, while having a flavor closer to a finite-volume method. This numerical approach not only uses structured/unstructured conformal meshes but also handles nonconformal meshes (h-adaptivity) with nonuniform approximation orders (p-adaptivity) in different regions, thus leading to high flexibility and efficiency for heterogeneous multiscale problems. To implement the discontinuous Galerkin algorithm, a concise but more general heterogeneous Riemann solver is provided to effectively and accurately resolve the coupling of multiple subdomains for both elastic–elastic/fluid–fluid and fluid–solid coupling. Finally, numerical results demonstrate the flexibility, high accuracy, and efficiency of our method for elastic-/acoustic-wave simulation. [ABSTRACT FROM PUBLISHER]

A stable high-order Runge-Kutta discontinuous Galerkin (RKDG) scheme that strictly preserves positivity of the solution is designed to solve the Boltzmann kinetic equation with model collision integrals. Stability is kept by accuracy of velocity discretization, conservative calculation of the discrete collision relaxation term, and a limiter. By keeping the time step smaller than the local mean collision time and forcing positivity values of velocity distribution functions on certain points, the limiter can preserve positivity of solutions to the cell average velocity distribution functions. Verification is performed with a normal shock wave at a Mach number 2.05, a hypersonic flow about a two-dimensional (2D) cylinder at Mach numbers 6.0 and 12.0, and an unsteady shock tube flow. The results show that, the scheme is stable and accurate to capture shock structures in steady and unsteady hypersonic rarefied gaseous flows. Compared with two widely used limiters, the current limiter has the advantage of easy implementation and ability of minimizing the influence of accuracy of the original RKDG method. [ABSTRACT FROM AUTHOR]

The simulation of unbounded domains inevitably requires an artificial truncation of the computational domain and spurious reflections resulting from this procedure are a common problem. In this paper, a perfectly matched layer formulation for Maxwell’s equations in purely hyperbolic form is presented. The model is applied to standard wave attenuation problems and particle-in-cell simulations of electron beam devices. [ABSTRACT FROM PUBLISHER]

An adaptive mesh refinement algorithm based on a continuous adjoint approach is developed. Both the primal equation and the adjoint equation are approximated with the discontinuous Galerkin (DG) method. The proposed adaptive algorithm is used in compressible Euler equations. Numerical tests are made to show the superiority of the proposed adaptive algorithm. [ABSTRACT FROM AUTHOR]

We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed based on a first-order hyperbolic advection–diffusion formulation of the target governing equations. We present, in details, the efficient construction of the proposed high-order schemes (called DG-H), and show that these schemes have the same number of global degrees-of-freedom as comparable conventional high-order DG schemes, produce the same or higher order of accuracy solutions and solution gradients, are exact for exact polynomial functions, and do not need a second-derivative diffusion operator. We demonstrate that the constructed high-order schemes give excellent quality solution and solution gradients on irregular triangular elements. We also construct a Weighted Essentially Non-Oscillatory (WENO) limiter for the proposed DG-H schemes and apply it to discontinuous problems. We also make some accuracy comparisons with conventional DG and interior penalty schemes. A relative qualitative cost analysis is also reported, which indicates that the high-order schemes produce orders of magnitude more accurate results than the low-order schemes for a given CPU time. Furthermore, we show that the proposed DG-H schemes are nearly as efficient as the DG and Interior-Penalty (IP) schemes as these schemes produce results that are relatively at the same error level for approximately a similar CPU time. [ABSTRACT FROM AUTHOR]

This paper presents a multi-dimensional high-order discontinuous Galerkin (DG) method in an arbitrary Lagrangian–Eulerian (ALE) formulation to simulate flows over variable domains with moving and deforming meshes. It is an extension of the gas-kinetic DG method proposed by the authors for static domains (X. Ren et al., 2015 [22] ). A moving mesh gas kinetic DG method is proposed for both inviscid and viscous flow computations. A flux integration method across a translating and deforming cell interface has been constructed. Differently from the previous ALE-type gas kinetic method with piecewise constant mesh velocity at each cell interface within each time step, the mesh velocity variation inside a cell and the mesh moving and rotating at a cell interface have been accounted for in the finite element framework. As a result, the current scheme is applicable for any kind of mesh movement, such as translation, rotation, and deformation. The accuracy and robustness of the scheme have been improved significantly in the oscillating airfoil calculations. All computations are conducted in a physical domain rather than in a reference domain, and the basis functions move with the grid movement. Therefore, the numerical scheme can preserve the uniform flow automatically, and satisfy the geometric conservation law (GCL). The numerical accuracy can be maintained even for a largely moving and deforming mesh. Several test cases are presented to demonstrate the performance of the gas-kinetic DG-ALE method. [ABSTRACT FROM AUTHOR]

This paper carries out systematical investigations on the performance of several typical shock-capturing schemes for the discontinuous Galerkin (DG) method, including the total variation bounded (TVB) limiter and three artificial diffusivity schemes (the basis function-based (BF) scheme, the face residual-based (FR) scheme, and the element residual-based (ER) scheme). Shock-dominated flows (the Sod problem, the Shu-Osher problem, the double Mach reflection problem, and the transonic NACA0012 flow) are considered, addressing the issues of accuracy, non-oscillatory property, dependence on user-specified constants, resolution of discontinuities, and capability for steady solutions. Numerical results indicate that the TVB limiter is more efficient and robust, while the artificial diffusivity schemes are able to preserve small-scale flow structures better. In high order cases, the artificial diffusivity schemes have demonstrated superior performance over the TVB limiter. [ABSTRACT FROM AUTHOR]

Discontinuous Galerkin (DG) finite element method was adopted for the numerical approximation of the Reynolds-averaged Navier-Stokes(RANS) equations with the Spalart-Allmaras turbulence model. In order to make the solver robust, the original turbulence model equation were modified accordingly. Furthermore, high order approximation of the real solid boundary was used and several layers of curved meshes were constructed to avoid inconsistent mesh cross-overs. For the computation of the distance of each quadrature point to the nearest curved wall boundaries, a fast straightforward numerical method was proposed. The DG discretization of the RANS equations were demonstrated for turbulent flows past a NACA0012 airfoil and RAE airfoil based on hybrid mesh. Numerical results indicate that highly accurate solutions can be obtained with the modified turbulent equation on coarse curved hybrid mesh. [ABSTRACT FROM AUTHOR]

For transient finite element analysis of eddy-current fields in solid rotors which have invariant material properties, it is convenient to use the Eulerian formulation where only a fixed mesh is needed when modeling motion effect. However, in the Eulerian formulation, a convection-diffusion equation instead of the pure diffusion equation has to be solved. Furthermore, when the rotor rotates at high speeds, the eddy-current fields usually have sharp transition layers over a period of time, thereby making it difficult to solve these fields accurately and effectively. To obtain a high-resolution numerical solution efficiently, an adaptive discontinuous Galerkin method is proposed and numerical examples are reported to showcase the accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we explore the accuracy limits of a finite-element time-domain (TD) method applied to the Maxwell equations, based on a discontinuous Galerkin scheme in space, and a leap-frog temporal integration. The dispersion and dissipation properties of the method are investigated, as well as the anisotropy of the errors. The results of this novel analysis are represented in a practical and comprehensible manner, useful for the application of the method, and for the understanding of the behavior of the errors in discontinuous Gelerkin TD methods. A comparison with the finite-difference TD method, in terms of computational cost, is also included. [ABSTRACT FROM AUTHOR]

We present the simulation of the transient excitation and evolution of a \TE34, 19 mode in the resonant cavity of the 170 GHz gyrotron. This gyrotron is planned for electron cyclotron resonance heating in the ITER tokamak fusion reactor. The numerical computation of a state-of-the-art gyrotron resonant cavity with a transient 3-D full wave particle-in-cell (PIC) method is a computationally demanding task. It was enabled by a highly scalable PIC scheme. To allow the numerical simulation of the high-frequency electromagnetic waves, we use a high-order discontinuous Galerkin method. [ABSTRACT FROM PUBLISHER]

Fast design codes for the simulation of the particle–field interaction in the interior of gyrotron resonators are available. They procure their rapidity by making strong physical simplifications and approximations, which are not known to be valid for many variations of the geometry and the operating setup. For the first time, we apply a fully electromagnetic (EM) transient 3-D high-order discontinuous Galerkin particle-in-cell method solving the complete self-consistent nonlinear Vlasov–Maxwell equations to simulate a 30-GHz high-power millimeter-wave gyrotron resonator without physical reductions. This is a computational expensive endeavor, which requires today's high-performance computing capacity. However, this enables a detailed analysis of the EM field, the excited \TE2, 3 mode, the frequencies, and the azimuthal particle bunching in the beam. Therefrom, we present new insights into the complex particle–field interaction of the electron cyclotron maser instability transferring kinetic energy from the electron beam to the EM field. [ABSTRACT FROM PUBLISHER]

This paper presents for the first time the transient simulation of the 3-D \TE34, 19 mode converter with surface deformation. The simulation results were obtained by solving the Maxwell equations directly on a 3-D domain with a discontinuous Galerkin method. The presented full-wave simulation was possible only through the use of an advanced highly scalable numerical method operating on a large-scale high-performance computing system. Moreover, the properties of the Maxwell solver with respect to accuracy and computation time are discussed for the application to a smooth-wall \TE34, 19 waveguide where an analytical solution is available. [ABSTRACT FROM PUBLISHER]