A Kernel-Based explicit unconditionally stable scheme for Hamilton-Jacobi equations on nonuniform meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:415

Article

Christlieb, Andrew¹  Sands, William¹  Yang, Hyoseon¹ 

[1] Michigan State Univ, Dept Computat Math Sci & Engn, E Lansing, MI 48824 USA

关键词: Kernel based scheme;    Unconditionally stable;    High order accuracy;    Weighted essentially non-oscillatory methodology;    Exponential basis;    Nonuniform meshes;   

DOI  :  10.1016/j.jcp.2020.109543

来源: Elsevier

【 摘 要 】

In [11], the authors developed a class of high-order numerical schemes for the Hamilton-Jacobi (H-J) equations, which are unconditionally stable, yet take the form of an explicit scheme. This paper extends such schemes, so that they are more effective at capturing sharp gradients, especially on nonuniform meshes. In particular, we modify the weighted essentially non-oscillatory (WENO) methodology in the previously developed schemes by incorporating an exponential basis and adapting the previously developed nonlinear filters used to control oscillations. The main advantages of the proposed schemes are their effectiveness and simplicity, since they can be easily implemented on higher-dimensional nonuniform meshes. We perform numerical experiments on a collection of examples, including H-J equations with linear, nonlinear, convex and non-convex Hamiltonians. To demonstrate the flexibility of the proposed schemes, we also include test problems defined on non-trivial geometry. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free