Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA discontinuous Galerkin overset scheme using WENO reconstruction and subcells for two-dimensional problems
82
0
0.0
(
0
)
Added by
S R Siva Prasad Kochi Mr
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A new scheme for communication between overset grids using subcells and Weighted Essentially Non Oscillatory (WENO) reconstruction for two-dimensional problems has been proposed. The effectiveness of this procedure is demonstrated using the discontinuous Galerkin method (DGM). This scheme uses WENO reconstruction using cell averages by dividing the immediate neighbors into subcells to find the degrees of freedom in cells near the overset interface. This also has the added advantage that it also works as a limiter if a discontinuity passes through the overset interface. Accuracy tests to demonstrate the maintenance of higher order are provided. Results containing shocks are also provided to demonstrate the limiter aspect of the data communication procedure.
rate research
Read More
Discontinuous Galerkin (DG) methods are extensions of the usual Galerkin finite element methods. Although there are vast amount of studies on DG methods, most of them have assumed shape-regularity conditions on meshes for both theoretical error analysis and practical computations. In this paper, we present a new symmetric interior penalty DG scheme with a modified penalty term. We show that, without imposing the shape-regularity condition on the meshes, the new DG scheme inherits all of the good properties of standard DG methods, and is thus robust on anisotropic meshes. Numerical experiments confirm the theoretical error estimates obtained.
In this paper, we generalize the compact subcell weighted essentially non oscillatory (CSWENO) limiting strategy for Runge-Kutta discontinuous Galerkin method developed recently by us in 2021 for structured meshes to unstructured triangular meshes. The main idea of the limiting strategy is to divide the immediate neighbors of a given cell into the required stencil and to use a WENO reconstruction for limiting. This strategy can be applied for any type of WENO reconstruction. We have used the WENO reconstruction proposed by Zhu and Shu in 2019 and provided accuracy tests and results for two-dimensional Burgers equation and two dimensional Euler equations to illustrate the performance of this limiting strategy.
In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods with the upwind scheme for the steady-state convection-diffusion-reaction problems over polytopic meshes. The optimal error estimates are provided in both diffusion-dominated and convection-dominated regimes. Furthermore, several numerical experiments are presented to verify the theoretical error estimates, and to well approximate boundary layers and/or internal layers.
We present a discontinuous Galerkin internal-penalty scheme that is applicable to a large class of linear and non-linear elliptic partial differential equations. The scheme constitutes the foundation of the elliptic solver for the SpECTRE numerical relativity code. As such it can accommodate (but is not limited to) elliptic problems in linear elasticity, general relativity and hydrodynamics, including problems formulated on a curved manifold. We provide practical instructions that make the scheme functional in a production code, such as instructions for imposing a range of boundary conditions, for implementing the scheme on curved and non-conforming meshes and for ensuring the scheme is compact and symmetric so it may be solved more efficiently. We report on the accuracy of the scheme for a suite of numerical test problems.
In this paper, we present a unified analysis of the superconvergence property for a large class of mixed discontinuous Galerkin methods. This analysis applies to both the Poisson equation and linear elasticity problems with symmetric stress formulations. Based on this result, some locally postprocess schemes are employed to improve the accuracy of displacement by order min(k+1, 2) if polynomials of degree k are employed for displacement. Some numerical experiments are carried out to validate the theoretical results.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
