A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 1: The 1-D case

Ramani, Raaghav; Reisner, Jon; Shkoller, Steve

doi:10.1016/j.jcp.2019.02.049

Cited by 18 publications

(50 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have additionally compared our simple numerical implementation with more sophisticated methods using higher order regularizations, and found good agreement (as in previous numerical studies [8,93]) between all three methods in predicting both the bubble and spike tip locations, as well as the radii and location of the spiral roll up structures. While our simple numerical method leads to a fast-running algorithm, in the future, more sophisticated numerical implementations of the z-model will be considered, including implementations of a fast summation method [45], a point-insertion procedure [57], non-oscillatory shock-capturing, and space-time smooth artificial viscosity [77].…”

Section: Discussionmentioning

confidence: 99%

“…These methods rely on a careful reconstruction of the numerical flux; centered numerical fluxes, such as the Lax-Friedrichs flux [60], add dissipation implicitly to preserve stability and monotonicity, while upwinding methods based upon exact or approximate Riemann solvers tend to be complex and computationally costly. We refer the reader to [77] and the references therein for further details. Explicit artificial viscosity methods provide a simple way to stabilize shock fronts and contact discontinuities.…”

Section: B the C-methods For Space-time Smooth Artificial Viscositymentioning

confidence: 99%

“…This is a spacetime smooth artificial viscosity method employed with a highly simplified WENO discretization of the compressible Euler equations (see[80,77,78]). 5 We note that both the CPU time and memory usage are approximately a factor of 2 larger for unsplit methods than for split methods[1].…”

mentioning

confidence: 99%

See 2 more Smart Citations

A multiscale model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Ramani

Shkoller

2020

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

We develop a novel multiscale model of interface motion for the Rayleigh-Taylor instability (RTI) and Richtmyer-Meshkov instability (RMI) for two-dimensional, inviscid, compressible flows with vorticity, which yields a fast-running numerical algorithm that produces both qualitatively and quantitatively similar results to a resolved gas dynamics code, while running approximately two orders of magnitude (in time) faster. Our multiscale model is founded upon a new compressible-incompressible decomposition of the velocity field u = v + w. The incompressible component w of the velocity is also irrotational and is solved using a new asymptotic model of the Birkhoff-Rott singular integral formulation of the incompressible Euler equations, which reduces the problem to one spatial dimension. This asymptotic model, called the higher-order z-model, is derived using small nonlocality as the asymptotic parameter, allows for interface turn-over and roll-up, and yields a significant simplification for the equation describing the evolution of the amplitude of vorticity. This incompressible component w of the velocity controls the small scale structures of the interface and can be solved efficiently on fine grids. Meanwhile, the compressible component of the velocity v remains continuous near contact discontinuities and can be computed on relatively coarse grids, while receiving subgrid scale information from w. We first validate the incompressible higher-order z-model by comparison with classical RTI experiments as well as full point vortex simulations. We then consider both the RTI and the RMI problems for our multiscale model of compressible flow with vorticity, and show excellent agreement with our high-resolution gas dynamics solutions. 4 Numerical implementation of the z-model 15

show abstract

Section: Discussionmentioning

confidence: 99%

Section: B the C-methods For Space-time Smooth Artificial Viscositymentioning

confidence: 99%

See 1 more Smart Citation

A multiscale model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Ramani

Shkoller

2020

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Algorithms that explicitly introduce diffusion provide a simple way to stabilize higherorder numerical schemes and subsequently remove non-physical oscillations near shocks. We refer the reader to the introductory sections in [20,18] for a review of the classical artificial viscosity method [36].…”

Section: Numerical Discretizationmentioning

confidence: 99%

“…

This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities.

…”

mentioning

confidence: 99%