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Title: | Recovery reconstruction at oblique interface in recovery-based discontinuous Galerkin | Authors: | Than Phuc Huynh | Keywords: | Recovery-based discontinuous Galerkin;Tensor-product;Minimal basis | Issue Date: | 2018 | Abstract: | The Recovery-based Discontinuous Galerkin (RDG) discretization was first introduced in 2005 by Prof. Bram van Leer (the University of Michigan, Ann Arbor)[7]. It has been proved to be one of the best Discontinuous Galerkin (DG) discretizations on Cartesian grids for diffusion problems[1]. Using a tensor-product basis, RDG demonstrated an order of accuracy 3p + 1 for odd p and 3p + 2 for even p, where p is the order of the polynomial basis used. These values of the order of accuracy are calculated from L2-norms of the errors of the function-value cell averages. They are true for both linear and nonlinear problems on a Cartesian grid. The key to the success of RDG is the so-called recovery function, normally denoted by f, which is centered at an interface. By construction, the recovery function f is indistinguishable in the weak sense from the two original numerical solutions from the two cells abutting the interface in question. Unlike those numerical solutions, however, the recovery function f is continuous across the interface, leading to unique interface quantities used for interface-flux calculations. Naturally, we have been working on extending RDG from Cartesian to triangular grids, but it has not been smooth sailing. We first encountered the problem of singular reconstruction of f with tensor-product basis. Switching to minimal basis has removed the singularity in the reconstruction of f, but the accuracy of the resulted method has suffered. The main reason is that a minimal basis contains less information than a corresponding tensor-product basis does. In this study, we are trying to determine what has gone awry with the tensor-product basis on triangles. (It has work so well on Cartesian.) We first start with two side-by-side squares, then the common interface is rotated by an angle α from the vertical line, forming an oblique common interface between two now quadrilaterals. Depending on the location of the pivot, the two squares will eventually morph into two right triangles, or one right trapezoid and one isosceles right triangle. We will then study how the reconstruction of the recovery function f changes with the rotation angle α |
URI(1): | http://epub.vgu.edu.vn/handle/dlibvgu/742 |
Appears in Collections: | Computational Engineering (CompEng) |
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Recovery reconstruction at oblique interface in recovery-based discontinuous Galerkin.pdf | 1.02 MB | Adobe PDF |
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