An arbitrary-order Runge-Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets

JOURNAL OF COMPUTATIONAL PHYSICS

卷:349

Article

Jibben, Z.¹  Herrmann, M.² 

[1] Los Alamos Natl Lab, Computat Phys & Methods CCS 2, Los Alamos, NM 87544 USA

[2] Arizona State Univ, Dept Mech & Aerosp Engn, Tempe, AZ 85287 USA

关键词: Discontinuous Galerkin;    Arbitrary order;    Conservative level set;    Multiphase flow;   

DOI  :  10.1016/j.jcp.2017.08.035

来源: Elsevier

【 摘 要 】

We present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method [18,19]. This represents an extension of the method recently proposed by Owkes and Desjardins[21], by solving the level set equations on the refined level set grid [9] and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k + 1 order convergence rate in the L-1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann[9]. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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