Bound - preserving modified exponential Runge - Kutta discontinuous Galerkin methods for scalar conservation laws with stiff source terms
نویسندگان
چکیده
In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar conservation laws with stiff source terms by extending the idea in Zhang and Shu [39]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.
منابع مشابه
Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge-Kutta Discontinuous Galerkin Method for Scalar Conservation Laws
In this paper we present the analysis for the Runge-Kutta discontinuous Galerkin (RKDG) method to solve scalar conservation laws, where the time discretization is the third order explicit total variation diminishing Runge–Kutta (TVDRK3) method. We use an energy technique to present the L-norm stability for scalar linear conservation laws, and obtain a priori error estimates for smooth solutions...
متن کاملA Runge-Kutta Discontinuous Galerkin Method with Conservation Constraints to Improve CFL Condition for Solving Conservation Laws
We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [7, 6, 5, 4] for conservation Laws. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. We use this new formulation to solve conservation laws on one-d...
متن کاملA Conservation Constrained Runge-Kutta Discontinuous Galerkin Method with the Improved CFL Condition for Conservation Laws
We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [6, 5, 4, 3] for conservation Laws. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. We use this new formulation to solve conservation laws on one-d...
متن کاملTVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
This is the second paper in a series in which we construct and analyze a class of TVB (total variation bounded) discontinuous Galerkin finite element methods for solving conservation laws ut + Ed I(fi(u))xi = 0. In this paper we present a general framework of the methods, up to any order of formal accuracy, using scalar one-dimensional initial value and initial-boundary problems as models. In t...
متن کامل