• Corpus ID: 233481389

A robust, high-order implicit shock tracking method for simulation of complex, high-speed flows

@article{Huang2021ARH,
  title={A robust, high-order implicit shock tracking method for simulation of complex, high-speed flows},
  author={Tianci Huang and Matthew J. Zahr},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.00139}
}
High-order implicit shock tracking (fitting) is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features, e.g., contact lines, shock waves, and rarefactions. These methods align elements of the computational mesh with non-smooth features to represent them perfectly, allowing high-order basis functions to approximate smooth regions of the solution without the need for nonlinear stabilization, which leads to accurate approximations on traditionally… 
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References

SHOWING 1-10 OF 46 REFERENCES
Implicit shock tracking using an optimizationbased high-order discontinuous Galerkin method
  • Journal of Computational Physics,
  • 2020
A moving discontinuous Galerkin finite element method for flows with interfaces
Sub-Cell Shock Capturing for Discontinuous Galerkin Methods
A shock capturing strategy for higher order Discontinuous Galerkin approximations of scalar conservation laws is presented. We show how the original explicit artificial viscosity methods proposed
A Simple Mesh Generator in MATLAB
Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) ...
A Least-Squares Formulation of the Moving Discontinuous Galerkin Finite Element Method with Interface Condition Enforcement
TLDR
This method combines MDG-ICE, which uses a weak formulation that separately enforces a conservation law and the corresponding interface condition and treats the discrete geometry as a variable, with the Discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan to systematically generate optimal test functions from the trial spaces of both the discrete flow field and discrete geometry.
The Moving Discontinuous Galerkin Finite Element Method with Interface Condition Enforcement for Compressible Viscous Flows
TLDR
The moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is applied to the case of viscous flows and is shown to accurately resolve and transport viscous structures without relying on numerical dissipation for stabilization.
High-Order Resolution of Multidimensional Compressible Reactive Flow Using Implicit Shock Tracking
A recently developed high-order implicit shock tracking method is novelly applied to a benchmark problem in two-dimensional compressible reactive flow, and results of remarkably high accuracy are a...
An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions
TLDR
This work advocates a gradient-based, full space solver where the mesh and conservation law solution converge to their optimal values simultaneously and therefore never require the solution of the discrete conservation law on a non-aligned mesh.
A novel stabilization method for high-order shock fitting with finite element methods
A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework
Dealing with strong shocks while retaining low numerical dissipation traditionally has been one of the major challenges for high order methods like discontinuous Galerkin (DG). In the literature,
...
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