Related papers: Preventing pressure oscillations does not fix loca…
In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used to determine the minimal amount of entropy stabilization…
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…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
In this work, we consider the discretization of nonlinear hyperbolic systems in nonconservative form with the high-order discontinuous Galerkin spectral element method (DGSEM) based on collocation of quadrature and interpolation points…
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…
In this paper, we present consistent and inconsistent discontinuous Galerkin methods for incompressible Euler and Navier-Stokes equations with the kinematic pressure, Bernoulli function and EMAC function. Semi- and fully discrete energy…
An implicit Euler discontinuous Galerkin scheme for the Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP) equation for population densities with no-flux boundary conditions is suggested and analyzed. Using an exponential variable…
High-order entropy-stable discontinuous Galerkin (DG) methods for nonlinear conservation laws reproduce a discrete entropy inequality by combining entropy conservative finite volume fluxes with summation-by-parts (SBP) discretization…
We present a high-order entropy stable discontinuous Galerkin (ESDG) method for nonlinear conservation laws on both multi-dimensional domains and on networks constructed from one-dimensional domains. These methods utilize treatments of…
We demonstrate that the shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Additionally, we show that the classical Newtonian slip friction and Manning…
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 the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
A framework for numerical evaluation of entropy-conservative volume fluxes in gas flows with internal energies is developed, for use with high-order discretization methods. The novelty of the approach lies in the ability to use arbitrary…
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability…
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…
We develop entropy dissipative higher order accurate local discontinuous Galerkin (LDG) discretizations coupled with Diagonally Implicit Runge-Kutta (DIRK) methods for nonlinear degenerate parabolic equations with a gradient flow structure.…
We present a novel class of locally conservative, entropy stable and well-balanced discontinuous Galerkin (DG) methods for the nonlinear shallow water equation with a non-flat bottom topography. The major novelty of our work is the use of…
In this paper, we present an entropy-stable (ES) discretization using a nodal discontinuous Galerkin (DG) method for the ideal multi-ion magneto-hydrodynamics (MHD) equations. We start by performing a continuous entropy analysis of the…