A High-Order Flux Reconstruction/Correction Procedure via Reconstruction Method for Shock Capturing with Space-Time Extension Time Stepping and Adaptive Mesh Refinement

2017 ◽  
Author(s):  
Xiaoliang Zhang ◽  
Chunlei Liang ◽  
Jingjing Yang
Keyword(s):  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Space Time ◽  
High Order ◽  
Shock Capturing ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Correction Procedure ◽  
Time Stepping ◽  
Time Extension

scholarly journals Research on high-order flux reconstruction method with adaptive mesh for shock capturing

2020 ◽  
Author(s):  
Xiuqiang Ma ◽  
Jian Xia ◽  
Hao Fu
Keyword(s):  
Adaptive Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
High Order ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Spectral Difference ◽  
High Order Schemes ◽  
Solution Methods ◽  
Long Time

Abstract High order schemes have been developed for a quite long time, and many famous schemes arise like Discontinuous Galerkin (DG), Spectral Difference (SD) and WENO schemes, etc. The Flux Reconstruction (FR) scheme proposed by Huynh has attracted the attention of researchers for its simplicity and efficiency. It’s written in differential form and bridges the DG and SD schemes, which can be constructed with a proper choice of parameter. In this paper, realize FR scheme based on the framework of the open source Adaptive Mesh Refinement (AMR) library p4est. To capture shock sharply, the performance of Localized Laplacian Artificial Viscosity (LLAV) and In-cell Piecewise Integrated Solution methods are compared. As an important way of reducing computational cost, AMR technique integrated in p4est is also combined with FR. The performance of the developed code is tested in both one dimensional and two dimensional and get some quite attracting results.

scholarly journals A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods

2021 ◽  
Author(s):  
Johannes Markert ◽  
Gregor Gassner ◽  
Stefanie Walch
Keyword(s):  
Discontinuous Galerkin ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
High Order ◽  
Shock Capturing ◽  
High Order Accuracy ◽  
Finite Volume Scheme ◽  
Galerkin Methods ◽  
Order Accuracy ◽  
New Strategy

AbstractIn this paper, a new strategy for a sub-element-based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low-to-high-order discretizations on this set of data, including a first-order finite volume scheme up to the full-order DG scheme. The different DG discretizations are then blended according to sub-element troubled cell indicators, resulting in a final discretization that adaptively blends from low to high order within a single DG element. The goal is to retain as much high-order accuracy as possible, even in simulations with very strong shocks, as, e.g., presented in the Sedov test. The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing. The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

A High-Order Flux Reconstruction Method for 2-D Vorticity Transport

2021 ◽  
Author(s):  
Adrin Gharakhani
Keyword(s):  
Finite Difference ◽  
Poisson Equation ◽  
Finite Difference Methods ◽  
Neumann Boundary ◽  
Normal Derivative ◽  
High Order ◽  
Benchmark Problems ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Vorticity Transport

Abstract A compact high-order finite difference method on unstructured meshes is developed for discretization of the unsteady vorticity transport equations (VTE) for 2-D incompressible flow. The algorithm is based on the Flux Reconstruction Method of Huynh [1, 2], extended to evaluate a Poisson equation for the streamfunction to enforce the kinematic relationship between the velocity and vorticity fields while satisfying the continuity equation. Unlike other finite difference methods for the VTE, where the wall vorticity is approximated by finite differencing the second wall-normal derivative of the streamfunction, the new method applies a Neumann boundary condition for the diffusion of vorticity such that it cancels the slip velocity resulting from the solution of the Poisson equation for the streamfunction. This yields a wall vorticity with order of accuracy consistent with that of the overall solution. In this paper, the high-order VTE solver is formulated and results presented to demonstrate the accuracy and convergence rate of the Poisson solution, as well as the VTE solver using benchmark problems of 2-D flow in lid-driven cavity and backward facing step channel at various Reynolds numbers.

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