Related papers: Entropy-stable and entropy-dissipative approximati…
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…
A fully discrete implicit scheme is proposed for the Swift-Hohenberg model, combining the third-order backward differentiation formula (BDF3) for the time discretization and the second-order finite difference scheme for the space…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
This paper studies fully discrete finite element approximations to the Navier-Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration two implicit-explicit second order backward differentiation…
We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic…
We generalize the explicit high-order positivity-preserving entropy stable spectral collocation schemes developed in Upperman 2023 and Yamaleev 2023 for the three-dimensional (3D) compressible Navier Stokes equations to a time implicit…
In this work, we consider the One-Fluid Two-Temperature Euler (OFTT-Euler) equations used for modeling non-equilibrium hydrodynamics. The model comprises a system of nonlinear hyperbolic partial differential equations with non-conservative…
In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities…
We propose a novel class of temporal high-order parametric finite element methods for solving a wide range of geometric flows of curves and surfaces. By incorporating the backward differentiation formulae (BDF) for time discretization into…
Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. In this work, we describe a discretization of viscous terms in the…
A fully discrete Lagrangian scheme for numerical solution of the nonlinear fourth order DLSS equation in one space dimension is analyzed. The discretization is based on the equation's gradient flow structure in the $L^2$-Wasserstein metric.…
In this paper, the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors [18,16,17] for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids is extended to…
Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for…
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show…
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
It is well known that the seven-step backward difference formula (BDF) is unstable for the parabolic equations, since it is not even zero-stable. However, a linear combination of two non zero-stable schemes, namely the seven-step BDF and…
This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and cell biology. We present a space-time…
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…