A local discontinuous Galerkin level set reinitialization with subcell stabilization on unstructured meshes[Formula presented]

2022-10-01
Karakuş, Ali
Chalmers, N.
Warburton, T.
© 2022 Elsevier LtdIn this paper we consider a level set reinitialization technique based on a high-order, local discontinuous Galerkin method on unstructured triangular meshes. A finite volume based subcell stabilization is used to improve the nonlinear stability of the method. Instead of the standard hyperbolic level set reinitialization, the flow of time Eikonal equation is discretized to construct an approximate signed distance function. Using the Eikonal equation removes the regularization parameter in the standard approach which allows more predictable behavior and faster convergence speeds around the interface. This makes our approach very efficient especially for banded level set formulations. A set of numerical experiments including both smooth and non-smooth interfaces indicate that the method experimentally achieves design order accuracy.
Computers and Mathematics with Applications

Suggestions

A GPU-accelerated adaptive discontinuous Galerkin method for level set equation
KARAKUS, A.; WARBURTON, T.; AKSEL, MEHMET HALUK; Sert, Cüneyt (2016-01-02)
This paper presents a GPU-accelerated nodal discontinuous Galerkin method for the solution of two- and three-dimensional level set (LS) equation on unstructured adaptive meshes. Using adaptive mesh refinement, computations are localised mostly near the interface location to reduce the computational cost. Small global time step size resulting from the local adaptivity is avoided by local time-stepping based on a multi-rate Adams-Bashforth scheme. Platform independence of the solver is achieved with an extens...
A Novel Alternating Cell Directions Implicit Method for the Solution of Incompressible Navier Stokes Equations on Unstructured Grids
Bas, O.; ÇETE, ALİ RUHŞEN; Mengi, S.; Tuncer, İsmail Hakkı; Kaynak, U. (2017-01-01)
In this paper, A Novel Alternating Cell Direction Implicit Method (ACDI) is researched which allows implementation of fast line implicit methods on quadrilateral unstructured meshes. In ACDI method, designated alternating cell directions are taken along a series of contiguous cells within the unstructured grid domain and used as implicit lines similar to Line Gauss Seidel Method (LGS). ACDI method applied earlier for the solution of potential flows is extended for the solution of the incompressible Navier-S...
A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows
Eroglu, Fatma G.; Kaya Merdan, Songül; Rebholz, Leo G. (Elsevier BV, 2017-10-01)
In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The projection-based VMS stabilization is added as a separate post-processing step to the standard POD approximation, and since the stabilization step is completely decoupled, the method can easily be incorporated into existing codes, and stabilization parameters can be tuned independe...
A local discontinuous Galerkin method for Dirichlet boundary control problems
Yücel, Hamdullah (null; 2018-10-20)
In this paper, we consider Dirichlet boundary control of a convection-diffusion equation with L 2 4 – 5 boundary controls subject to pointwise bounds on the control posed on a two dimensional convex polygonal domain. 6 We use the local discontinuous Galerkin method as a discretization method. We derive a priori error estimates for 7 the approximation of the Dirichlet boundary control problem on a polygonal domain. Several numerical results are 8 provided to illustrate the theoretical results.
A shape deformation algorithm for constrained multidimensional scaling
Sahillioğlu, Yusuf (2015-12-01)
We present a new Euclidean embedding technique based on volumetric shape registration. Extrinsic representation of the intrinsic geometry of a shape is preferable in various computer graphics applications as it poses only a small degrees of freedom to deal with during processing. A popular Euclidean embedding approach to achieve such a representation is multidimensional scaling (MDS), which, however, distorts the original geometric details drastically. Our method introduces a constraint on the original MDS ...
Citation Formats
A. Karakuş, N. Chalmers, and T. Warburton, “A local discontinuous Galerkin level set reinitialization with subcell stabilization on unstructured meshes[Formula presented],” Computers and Mathematics with Applications, vol. 123, pp. 160–170, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85136689287&origin=inward.