Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows

Ching, Eric J.; Lv, Yu; Gnoffo, Peter A.; Barnhardt, Michael; Ihme, Matthias

doi:10.1016/j.jcp.2018.09.016

Cited by 75 publications

(33 citation statements)

References 35 publications

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“…Finally, a scalable preconditioning strategy will need to be developed in order to solve large‐scale problems using an iterative linear solver for which a direct solver is prohibitively expensive. Improved grid modifications, including local adaptivity, smoothing, and untangling, as well as scalable linear solvers will enable MDG‐ICE to be applied to three‐dimensional problems that include shock‐boundary layer interactions and validated against both experimental data and previously reported results 101‐103 …”

Section: Discussionmentioning

confidence: 99%

The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows

Kercher

Corrigan

Kessler

2021

Numerical Methods in Fluids

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The moving discontinuous Galerkin finite element method with interface condition enforcement is applied to the case of viscous flows. This method uses a weak formulation that separately enforces the conservation law, constitutive law, and the corresponding interface conditions in order to provide the means to detect interfaces or underresolved flow features. To satisfy the resulting overdetermined weak formulation, the discrete domain geometry is introduced as a variable, so that the method implicitly fits a priori unknown interfaces and moves the grid to resolve sharp, but smooth, gradients, achieving a form of anisotropic curvilinear r‐adaptivity. This approach avoids introducing low‐order errors that arise using shock capturing, artificial dissipation, or limiting. The utility of this approach is demonstrated with its application to a series of test problems culminating with the compressible Navier–Stokes solution to a Mach 5 viscous bow shock for a Reynolds number of 105 in two‐dimensional space. Time accurate solutions of unsteady problems are obtained via a space‐time formulation, in which the unsteady problem is formulated as a higher dimensional steady space‐time problem. The method is shown to accurately resolve and transport viscous structures without relying on numerical dissipation for stabilization.

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Section: Discussionmentioning

confidence: 99%

The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows

Kercher

Corrigan

Kessler

2021

Numerical Methods in Fluids

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“…To evaluate integrals, we use standard Gaussian quadrature with an order of accuracy no less than 2p + 1, where p is the user-prescribed order of the Lagrange polynomials. To capture shocks, intraelement pressure variations are used for shock detection while smooth artificial viscosity is used for stabilization [11].…”

Section: B Discontinuous Galerkin Discretizationmentioning

confidence: 99%

Sensitivity study of high-speed dusty flows over blunt bodies simulated using a discontinuous Galerkin method

Ching

Ihme

2019

AIAA Scitech 2019 Forum

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Recent interest in human-scale Mars missions has motivated research into the effects of dust particles that are suspended in the Martian atmosphere on reentry vehicles. For instance, these dust particles can enhance erosion of thermal protection systems and amplify surface heat fluxes. As such, in this work, we perform numerical simulations of hypersonic dusty flows over a blunt body using a two-way-coupled Lagrangian particle method in a discontinuous Galerkin framework. Due to the lack of a well-established physical model of the disperse phase appropriate for this multiphase flow regime, we aim to evaluate the sensitivities of numerically predicted dust-induced heat flux augmentation to various components and parameters of the model. Specifically, we investigate the drag coefficient correlation, the Nusselt number correlation, different terms in the particle momentum and energy equations, and particle size.

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“…It is important to note that these choices involving the element type, basis functions, and approximation of inner products all have a major impact on the performance of the resulting DG scheme in terms of computational complexity and robustness due, e.g., to the presence of spurious oscillations near discontinuities that result in unphysical solution states (like negative density or pressure) or aliasing instabilities. Many mechanisms exist in the DG community to combat spurious oscillations (i.e., shock capturing) such as slope [3,5,35] or WENO [36,37] limiters, filtering [29,38,39], finite volume sub-cells [40][41][42], MOOD-type limiting [43][44][45][46][47], or artificial viscosity [48,49]. The issue of shock capturing will not be discussed further.…”

Section: A Brief Introduction To Dgmentioning

confidence: 99%

A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?

Gassner

Winters

2021

Front. Phys.

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In this paper we will review a recent emerging paradigm shift in the construction and analysis of high order Discontinuous Galerkin methods applied to approximate solutions of hyperbolic or mixed hyperbolic-parabolic partial differential equations (PDEs) in computational physics. There is a long history using DG methods to approximate the solution of partial differential equations in computational physics with successful applications in linear wave propagation, like those governed by Maxwell’s equations, incompressible and compressible fluid and plasma dynamics governed by the Navier-Stokes and the Magnetohydrodynamics equations, or as a solver for ordinary differential equations (ODEs), e.g., in structural mechanics. The DG method amalgamates ideas from several existing methods such as the Finite Element Galerkin method (FEM) and the Finite Volume method (FVM) and is specifically applied to problems with advection dominated properties, such as fast moving fluids or wave propagation. In the numerics community, DG methods are infamous for being computationally complex and, due to their high order nature, as having issues with robustness, i.e., these methods are sometimes prone to crashing easily. In this article we will focus on efficient nodal versions of the DG scheme and present recent ideas to restore its robustness, its connections to and influence by other sectors of the numerical community, such as the finite difference community, and further discuss this young, but rapidly developing research topic by highlighting the main contributions and a closing discussion about possible next lines of research.

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Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows

Cited by 75 publications

References 35 publications

The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows

The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows

Sensitivity study of high-speed dusty flows over blunt bodies simulated using a discontinuous Galerkin method

A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?

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