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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:387

Article

Ramani, Raaghav¹  Reisner, Jon²  Shkoller, Steve¹ 

[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA

[2] Los Alamos Natl Lab XCP 4 MSF605, Los Alamos, NM 87544 USA

关键词: Gas dynamics;    Shocks and contacts;    Euler equations;    Artificial viscosity;    Shock collision;    Noise indicator;   

DOI  :  10.1016/j.jcp.2019.02.049

来源: Elsevier

【 摘 要 】

In this first part of two papers, we extend the C-method developed in [40] 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 [41]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free