Related papers: Enhanced HLLEM and HLL-CPS schemes for all Mach nu…
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are…
In this work, we introduce two novel reformulations of a recent weakly hyperbolic model for two-phase flow with surface tension. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a…
We describe a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamics code based on the total variation diminishing scheme. Contributions from ambipolar diffusion terms…
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
We recently derived analytical expressions for the pairwise (auto)correlation functions (CFs) between modular layers (MLs) in close-packed structures (CPSs) for the wide class of stacking processes describable as hidden Markov models (HMMs)…
Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…
We introduce a new scheme adaption strategy for one- and two-dimensional hyperbolic systems of conservation laws. The proposed approach builds upon the adaptive framework introduced in [S. Chu, A. Kurganov, and I. Menshov, Appl. Numer.…
Magnetohydrodynamic (MHD) simulations of subsonic (Mach number~$<1$) turbulence are crucial to our understanding of several processes including oceanic and atmospheric flows, the amplification of magnetic fields in the early universe,…
The evolutionarity conditions for the MHD shock waves are considered within the framework of the 8-moment approximation for collisionless plasma with heat fluxes. In the general case, evolutionarity diagrams are obtained depending on the…
The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid…
We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation…
We have developed a Monte Carlo technique for self-consistently calculating the hydrodynamic structure of oblique, steady-state shocks, together with the first-order Fermi acceleration process and associated non-thermal particle…
We present a convergence analysis of a finite volume (FV) scheme for the multicomponent compressible Euler system in the framework of dissipative weak (DW) solutions. DW solutions were introduced as a generalized solution framework in…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
In this paper, we derive optimal L2- and H1-norm error estimates for a fully discrete convex-splitting decoupled finite element method (FEM) for the two-phase diffuse interface magnetohydrodynamics (MHD) system. We use the semi-implicit…
We introduce a modified SPH approach that is based on discretising the particle density instead of the mass density. This approach makes it possible to use SPH particles with very different masses to simulate multi-phase flows with large…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
Ultra-lean premixed hydrogen combustion is a possible solution to decarbonize industry, while limiting flame temperatures and thus nitrous oxide emissions. These lean hydrogen/air flames experience strong preferential diffusion effects,…
In this paper we present three different numerical approaches to account for curl-type involution constraints in hyperbolic partial differential equations for continuum physics. All approaches have a direct analogy to existing and…
We report simulations of diffusive particle acceleration in oblique magnetohydrodynamical (MHD) shocks. These calculations are based on extension to oblique shocks of a numerical model for ``thermal leakage'' injection of particles at low…