Artificial Viscosity -- Then and Now

Margolin, L. G.; Lloyd‐Ronning, Nicole M.

doi:10.48550/arxiv.2202.11084

Cited by 2 publications

(3 citation statements)

References 46 publications

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“…They are the oldest methods for discontinuity capturing. The recent work of Margolin & Lloyd-Ronning [49] presents a comprehensive overview of and a new perspective on artificial viscosity methods. The method of Cook & Cabot (2005) [50] also belongs to such an approach.…”

Section: Artificial Viscosity Methodsmentioning

confidence: 99%

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Numerical Dissipation Control in High-Order Methods for Compressible Turbulence: Recent Development

Yee,

Sjögreen

2024

Fluids

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This comprehensive overview presents our continued efforts in high-order finite difference method (FDM) development for adaptive numerical dissipation control in the long-time integration of direct numerical simulation (DNS), large eddy simulation (LES), and implicit LES (ILES) computations of compressible turbulence for gas dynamics and MHD. The focus is on turbulence with shock wave numerical simulations using the adaptive blending of high-order structure-preserving non-dissipative methods (classical central, Padé (compact), and dispersion relation-preserving (DRP)) with high-order shock-capturing methods in such a way that high-order shock-capturing methods are active only in the vicinity of shock/shear waves, and high-gradient and spurious high-frequency oscillation regions guided via flow sensors. Any efficient and high-resolution high-order shock-capturing methods are good candidates for the blending of methods procedure. Typically, the adaptive blending of more than one method falls under two camps: hybrid methods and nonlinear filter methods. They are applicable to unstructured finite volume, finite element, discontinuous Galerkin, and spectral element methods. This work represents the culmination of over 20 years of high-order FDM developments and hands-on experience by the authors and collaborators in adaptive numerical dissipation control using the “high order nonlinear filter approach”. Extensions of these FDM versions to curvilinear nonuniform, freestream-preserving moving grids and time-varying deforming grids were also developed. By examining the construction of these two approaches using the high-order multistage type of temporal discretization, the nonlinear filter approach is made more efficient and less CPU-intensive while obtaining similar accuracy. A representative variety of test cases that compare the various blending of high-order methods with standalone standard methods is illustrated. Due to the fact that our nonlinear filter methods are not well known in compressible turbulence with shock waves, the intent of this comprehensive overview is for general audiences who are not familiar with our nonlinear filter methods. For readers interested in the implementation of our methods into their computer code, it is hoped that the long overview will be helpful.

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Section: Artificial Viscosity Methodsmentioning

confidence: 99%

“…Then, the logarithmic average of ρ/p required in the energy flux is defined via (49) with ρ/p replacing ρ.…”

Section: Tadmor-type Entropy-conserving Numerical Flux Using the Entr...mentioning

confidence: 99%

Numerical Dissipation Control in High-Order Methods for Compressible Turbulence: Recent Development

Yee,

Sjögreen

2024

Fluids

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“…Therefore, we employ the canonical "shock viscosity," Q, which was introduced by von Neumann and Richtmyer. 60 Here, we use the form of the shock viscosity given by Wilkins 61 (which is used in LS-DYNA, 62 see other works [63][64][65] for additional forms):…”

Section: Shock Viscosity For Stabilizing Dynamic Solution Of High Str...mentioning

confidence: 99%

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

Irwin,

Clayton,

Regueiro

2024

Numerical Meth Engineering

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A large deformation, coupled finite‐element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain‐rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one‐dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed‐form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain‐rate, and (iii) showing differences in deformations between a single‐phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain‐rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single‐phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain‐rate loading of soft porous materials. It was discovered that explicit, adaptive time‐stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time‐stepping schemes for shock‐like loadings. Shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.

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Artificial Viscosity -- Then and Now

Cited by 2 publications

References 46 publications

Numerical Dissipation Control in High-Order Methods for Compressible Turbulence: Recent Development

Numerical Dissipation Control in High-Order Methods for Compressible Turbulence: Recent Development

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

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