Search

Abstract We present in this paper a novel numerical method for the simulation of time-dependent, diluted spray combustion problems. Spray combustion is a complex numerical problem owing to the diversity of the phenomena (convection, diffusion, heat transfer, vaporization of droplets and chemical reaction) and the disparity of the scales involved. Our model considers a large number of tiny droplets (liquid phase) surrounded by a gas flow (gas phase), making up a special two-phase system where droplet interaction is neglected on account of the much larger inter-droplet distance compared to the droplet radius typically found in burners. The mathematical formulation of the problem follows a hybrid, Eulerian–Lagrangian approach: the continuous, gas phase is ruled by the conservation equations of mass, momentum, species mass fractions and energy, while the liquid phase is described by a set of ordinary differential equations (ODE) that govern the properties of each droplet along its fluid trajectory. For the resolution of the conservation equations of the gas phase, a Lagrange–Galerkin method in an anisotropic adaptive finite element framework is used. In combination with the aforementioned Lagrange–Galerkin methodology we apply a second order Explicit Runge–Kutta–Chebyshev scheme, also useful to solve the ODE systems of equations for the droplets movement. Explicit Runge–Kutta–Chebyshev preserves numerical stability while also facilitating a decoupled calculation of the unknown variables of the gas and liquid phases, a most beneficial feature from a computationally point of view. Finally, we show several examples to highlight the capabilities of our numerical algorithm in canonical and real-world configurations. Highlights • Eulerian–Lagrangian formulation for time-dependent, spray combustion problems. • Lagrange–Galerkin numerical scheme in anisotropic adaptive finite element for gas phase. • Lagrange–Galerkin scheme decouples Navier–Stokes from the energy/species mass fraction conservation equations. • Ex-RKC tackles coupled, highly-stiff, non-linear systems with enhanced numerical stability. • Simulations of canonical and real-world spray combustion configurations. [ABSTRACT FROM AUTHOR]

Abstract We introduce in this paper 'A-SLEIPNNIR' ("Adaptive Semi-Lagrangian Ensemble Implementation of Particle level set for Newtonian and non-Newtonian Interfacial Rheology"). The proposed method combines a semi-Lagrangian approach for the transport operator, a particle level set technique for interface capturing featuring second-order accurate redistancing, and anisotropic mesh refinement for spatial resolution. The high-order, quadratic Finite Element discretization, together with an a posteriori error analysis produce a metric tensor that is passed on to an anisotropic mesh generator. We explore the peculiar features of the numerical scheme such as the impact of the marker particles, the reinitialization procedure or the Adaptive Mesh Refinement (AMR) strategy, in a series of benchmark problems for the solution of the interface transport equation with analytically supplied, divergence-free velocity fields. The results show that our approach yields an accurate and robust, yet computationally inexpensive framework for moving interfaces suitable for Scientific and Engineering applications. Highlights • Anisotropic, particle level set technique for moving interfaces. • Semi-Lagrangian, finite element implementation with quadratic polynomials. • Anisotropic mesh refinement offers accuracy similar to isotropic at a lower cost. • Marker particles provide enhanced shape preservation. • Robustness, accuracy, flexibility and efficiency in pure advection problems. [ABSTRACT FROM AUTHOR]

We propose in this paper an anisotropic, adaptive, finite element algorithm for steady, linear advection-diffusion-reaction problems with strong anisotropic features. The error analysis is based on the dual weighted residual methodology, allowing us to perform "goal-oriented" adaptation of a certain functional J(u) of the solution and derive an "optimal" metric tensor for local mesh adaptation with linear and quadratic finite elements. As a novelty, and to evaluate the weights of the error estimator on unstructured meshes composed of anisotropic triangles, we make use of a patchwise, higher-order interpolation recovery readily extendable to finite elements of arbitrary order. We carry out a number of numerical experiments in two dimensions so as to prove the capabilities of the goal-oriented adaptive method. We compute the convergence rate and the effectivity index for a series of output functionals of the solution. The results show the good performance of the algorithm with linear as well as quadratic finite elements. [ABSTRACT FROM AUTHOR]