Related papers: Entropy conserving/stable schemes for a vector-kin…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…
We design and analyse an energy stable, structure preserving and well-balanced scheme for the Ripa system of shallow water equations. The energy stability of the numerical solutions is achieved by introducing appropriate stabilisation terms…
We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When…
This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
In this paper, we present a shock capturing discontinuous Galerkin (SC-DG) method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time…
We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the…
This paper deals with a splitting method applied to a conservation law model of manufacturing system incorporating yield loss. A splitting scheme has been proposed. The yield loss term is treated by solving implicitly an ordinary…
High order methods based on diagonal-norm summation by parts operators can be shown to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of hyperbolic PDEs. These methods can also be interpreted as nodal…
Since the celebrated theorem of Lax and Wendroff, we know a necessary condition that any numerical scheme for hyperbolic problem should satisfy: it should be written in flux form. A variant can also be formulated for the entropy. Even…
We propose inflow and outflow boundary conditions for the compressible Navier-Stokes equations and prove that they allow a priori estimates of the entropy, mass and total energy. Furthermore, we demonstrate how to approximate these boundary…
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…
This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates,…
Hyperbolic-parabolic partial differential equations are widely used for the modeling of complex, multiscale problems. High-order methods such as the discontinuous Galerkin (DG) scheme are attractive candidates for their numerical…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features, and have traditionally required additional filtering, limiting, or artificial viscosity to avoid solution blow up.…
We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieved using the weighted essentially non-oscillatory (WENO)…
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly…
In this work, we study the slow entropy type invariant of a dynamical system proposed by A. M. Vershik. We provide an explicit construction of a system whose class of scaling entropy sequences is empty. For this unstable case, we introduce…
We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…