Related papers: A Moving Boundary Flux Stabilization Method for Ca…
For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
We present new stabilization terms for solving the linear transport equation on a cut cell mesh using the discontinuous Galerkin (DG) method in two dimensions with piecewise linear polynomials. The goal is to allow for explicit time…
We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel…
Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…
Computational fluid dynamics (CFD) studies have been increasingly used for blood flow simulations in intracranial aneurysms (ICAs). However, despite the continuous progress of body-fitted CFD solvers, generating a high quality mesh is still…
A parallel dynamic overset framework has been developed for the curvilinear immersed boundary (overset-CURVIB) method to enable tackling a wide range of challenging flow problems. The dynamic overset grids are used to locally increase the…
We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that…
Nonnegative directional splittings of anisotropic diffusion operators in the divergence form are investigated. Conditions are established for nonnegative directional splittings to hold in a neighborhood of an arbitrary interior point. The…
Centered finite-difference discretizations of convection--diffusion equations may oscillate when convection dominates at the mesh scale. For homogeneous Dirichlet problems with constant coefficients on uniform Cartesian grids, we derive…
The entropy conservative/stable algorithm of Friedrich~\etal (2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids for the compressible Euler equations. The primary…
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…
We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal…
Our goal is to develop a flux limiter of the Flux-Corrected Transport method for a nonconservative convection-diffusion equation. For this, we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a…
We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…
We present stability and error analysis for algebraic flux correction schemes based on monolithic convex limiting. For a continuous finite element discretization of the time-dependent advection equation, we prove global-in-time existence…
In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising…
In this paper we develop a conservative sharp-interface method dedicated to simulating multiple compressible fluids. Numerical treatments for a cut cell shared by more than two materials are proposed. First, we simplify the interface…