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

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

DOI:https://doi.org/10.1016/j.jcp.2019.02.049· OSTI ID:1501804

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)

In this first part of two papers, we extend 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 in one space dimension. For gas dynamics, the C-method couples the Euler equations to a scalar reaction-diffusion equation, whose solution C serves as a space-time smooth artificial viscosity indicator. The purpose of this paper is the development of a high-order numerical algorithm for shock-wall collision and bounce-back. Specifically, we generalize the original C-method by adding a new collision indicator, which naturally activates during shock-wall collision. Additionally, we implement a new high-frequency 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 show that our scheme improves the order of accuracy of our WENO algorithm, handles extremely strong discontinuities (ranging up to nine orders of magnitude), allows for shock collision and bounce back, and removes high frequency noise. The causes of the well-known “wall heating” phenomenon are discussed, and we demonstrate that this particular pathology can be effectively treated in the framework of the C-method. This method is generalized to two space dimensions in the second part of this work.

• 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: 1501804
• Alternate ID(s): OSTI ID: 1636001
• Report Number(s): LA-UR-18-22224
• Journal Information: Journal of Computational Physics, Vol. 387, Issue C; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
shocks
contacts
artificial viscosity