A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 2: The 2-D case

Ramani, Raaghav; Reisner, Jon; Shkoller, Steve

doi:10.1016/j.jcp.2019.02.048

Cited by 18 publications

(27 citation statements)

References 28 publications

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“…A fourth-order central difference approximation is used to compute the pressure gradient ∇p, while a second-order central difference approximation is employed to compute the diffusion terms (60). For brevity, we omit further details of the numerical implementation of the C-method and refer the reader to Appendix B and [78] for further details.…”

Section: Numerical Implementation Of the C-methodsmentioning

confidence: 99%

“…For the purposes of brevity, we have omitted some of the details and refer the reader to [78] for further discussion of the C-method in 2-D.…”

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

confidence: 99%

“…We spatially discretize the equations of motion, then use a standard thirdorder explicit Runge-Kutta solver for time integration. We shall use a space-time smooth artificial viscosity method, which we call the C-method [78], for the compressible v-equations (28) to stabilize shock fronts and contact discontinuities, and thereby prevent the onset of Gibbs oscillations. It remains to describe the following: first, the numerical implementation of the space-time smooth artificial viscosity C-method; second, the computation of the velocity w on the plane; third, the bilinear interpolation scheme; and finally, the calculation of the weak baroclinic term ∇p⋅∂ α z ρ .…”

Section: Numerical Implementation Of the Multiscale Algorithmmentioning

confidence: 99%

“…Periodic conditions are applied in the horizontal direction x 1 , while free-flow conditions are applied at the boundaries in the x 2 direction. In [78], we used the anisotropic C-method to solve this problem; the resulting solutions have the classic mushroom-shaped interface profile without overly diffused KHI roll-up regions and mixing zones. We shall use this solution, computed on a fine mesh of 50 × 200 cells with CFL ≈ 0.1 as our high resolution reference solution 6 .…”

Section: The Compressible Rti Test Of Liska and Wendroffmentioning

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].…”

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confidence: 99%

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

Ramani

Shkoller

2020

Journal of Computational Physics

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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

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Section: Numerical Implementation Of the C-methodsmentioning

confidence: 99%

“…For the purposes of brevity, we have omitted some of the details and refer the reader to [78] for further discussion of the C-method in 2-D.…”

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

confidence: 99%

Section: Numerical Implementation Of the Multiscale Algorithmmentioning

confidence: 99%

Section: The Compressible Rti Test Of Liska and Wendroffmentioning

confidence: 99%

mentioning

confidence: 99%

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

Ramani

Shkoller

2020

Journal of Computational Physics

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Informed Multi-scale Approach Applied to the British Columbia Fires of Late Summer 2017

Reisner

Josephson

Gorkowski

et al. 2022

Preprint

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Pyrocumulonimbus clouds have a complex origin depending on fire dynamics and meteorological conditions. When a pyrocumulonimbus (PyroCb) cloud formation develops and is maintained over a period of time, it can inject significant aerosol into the troposphere and lower stratosphere, resulting in longer term (months to years) climate cooling effects. In this work we investigate the British Columbia and northern Washington wildfires on August 12-13, 2017 using a multi-scale simulation framework. We use the output of a physics based wildfire model (FIRETEC) with parameterized energy, particle, and gas emissions to drive the upper atmospheric aerosol mass injection within a regional cloud resolving model (HIGRAD). We demonstrate that vertical motions produced by latent heat release of the condensation of ice and cloud particles within the PyroCbs induce another 5 km of lifting of the simulated aerosol plume. Primary black carbon and organic aerosols alone may not be enough to explain the observed aerosol burden, thus we show that dust and ash particles can enhance lofted aerosol mass. Additionally, we show that semi volatile organic gases emitted by the fires eventually condense, further increasing the aerosol burden. A simulation with all aerosol mechanisms active, driven by the observed fuel load and environmental conditions, reasonably reproduces an aerosol profile inferred from observational data.

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A Combination of Residual Distribution and the Active Flux Formulations or a New Class of Schemes That Can Combine Several Writings of the Same Hyperbolic Problem: Application to the 1D Euler Equations

Abgrall

2022

Commun. Appl. Math. Comput.

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We show how to combine in a natural way (i.e., without any test nor switch) the conservative and non-conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different classes of schemes: the residual distribution one (Abgrall in Commun Appl Math Comput 2(3): 341–368, 2020), and the active flux formulations (Eyman and Roe in 49th AIAA Aerospace Science Meeting, 2011; Eyman in active flux. PhD thesis, University of Michigan, 2013; Helzel et al. in J Sci Comput 80(3): 35–61, 2019; Barsukow in J Sci Comput 86(1): paper No. 3, 34, 2021; Roe in J Sci Comput 73: 1094–1114, 2017). The solution is globally continuous, and as in the active flux method, described by a combination of point values and average values. Unlike the “classical” active flux methods, the meaning of the point-wise and cell average degrees of freedom is different, and hence follow different forms of PDEs; it is a conservative version of the cell average, and a possibly non-conservative one for the points. This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem. We also develop a method to perform non-linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.

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A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 2: The 2-D case

Cited by 18 publications

References 28 publications

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

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

Informed Multi-scale Approach Applied to the British Columbia Fires of Late Summer 2017

A Combination of Residual Distribution and the Active Flux Formulations or a New Class of Schemes That Can Combine Several Writings of the Same Hyperbolic Problem: Application to the 1D Euler Equations

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