Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems

TL;DR: A monolithic approach to convex limiting in continuous finite element schemes for linear advection equations, nonlinear scalar conservation laws, and hyperbolic systems with built-in convex limiters to resolve steep fronts in a sharp and nonoscillatory manner is introduced.

TL;DR: High-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using a subcell flux corrections and convex limiting methodology are developed.

TL;DR: In this article, projection-based hyper-reduced models of nonlinear conservation laws are introduced, which inherit a semi-discrete entropy inequality independently of the choice of basis and choice of parameters.

TL;DR: In this paper , a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes is presented, which can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy.

TL;DR: This paper reviews and further develops a class of strong stability-preserving high-order time discretizations for semidiscrete method of lines approximations of partial differential equations, and builds on the study of the SSP property of implicit Runge--Kutta and multistep methods.

TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.

TL;DR: A class of explicit, Eulerian finite-difference algorithms for solving the continuity equation which are built around a technique called “flux correction,” which yield realistic, accurate results.

TL;DR: In this article, a new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains.