Imposing jump conditions on nonconforming interfaces for the Correction Function Method: A least squares approach

JOURNAL OF COMPUTATIONAL PHYSICS

卷:397

Article

Marques, Alexandre Noll¹  Nave, Jean-Christophe²  Rosales, Rodolfo Ruben³ 

[1] MIT, Dept Aeronaut & Astronaut, Cambridge, MA 02139 USA

[2] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada

[3] MIT, Dept Math, Cambridge, MA 02139 USA

关键词: Correction Function Method;    Embedded interface;    Poisson's equation;    High accuracy;    Gradient-Augmented Level Set Method;   

DOI  :  10.1016/j.jcp.2019.108869

来源: Elsevier

【 摘 要 】

We introduce a technique that simplifies the problem of imposing jump conditions on interfaces that are not aligned with a computational grid in the context of the Correction Function Method(CFM). The CFM offers a general framework to solve Poisson's equation in the presence of discontinuities to high order of accuracy, while using a compact discretization stencil. A key concept behind the CFM is enforcing the jump conditions in a least squares sense. This concept requires computing integrals over sections of the interface, which is a challenge in 3-D when only an implicit representation of the interface is available (e.g., the zero contour of a level set function). The technique introduced here is based on a new formulation of the least squares procedure that relies only on integrals over domains that are amenable to simple quadrature after local coordinate transformations. We incorporate this technique into a fourth order accurate implementation of the CFM, and show examples of solutions to Poisson's equation with imposed jump conditions computed in 2-D and 3-D. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free