Using an adaptive mesh high-order finite volume method to solve three hyperbolic conservation laws with diffusion or source term. (English) Zbl 1474.65313
Summary: After using the adaptive mesh finite volume method in [L. Kassiénou et al., Far East J. Appl. Math. 95, No. 4, 283–310 (2016; Zbl 1360.65223)] according to H. Tang and T. Tang [SIAM J. Numer. Anal. 41, No. 2, 487–515 (2003; Zbl 1052.65079)] and [A. van Dam, “Moving meshes and solution monitoring for compressible flow simulation”, Scientific Research (NWO) project 613.002.055 (2009)] to solve three test problems, we noticed that the numerical solutions are not sufficiently accurate. Those three problems are the following: a Burger’s problem with a diffusion term, a problem of two waves traveling in opposite directions with a source term and the SOD’s Shock Tube Problem with a diffusion term. The purpose in this paper is to improve the accuracy of the numerical solutions by using a high-order scheme in the finite volume method.
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
