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

Journal Article · Thu Mar 07 00:00:00 EST 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.02.048· OSTI ID:1501807

Ramani, Raaghav ^[1]; Reisner, Jon ^[2]; Shkoller, Steve  ^[1]

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1. Univ. of California, Davis, CA (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

This is the second part to our companion paper. Herein, we generalize to two space dimensions the C-method developed in for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. Solutions to our C-equations not only indicate the location of the shocks and contacts, but also track the geometry of the evolving fronts. This allows us to implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. To test the methodology, we use a highly simplified WENO-based discretization scheme. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska & Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-oscillatory solution, even though our simplified WENO-type scheme fails to run for this problem.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Nonproliferation
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1501807
• Alternate ID(s): OSTI ID: 1635993
• Report Number(s): LA-UR-18-24730
• Journal Information: Journal of Computational Physics, Vol. 387, Issue C; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Shocks