Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:332

Article

Chaudhuri, A.¹  Jacobs, G. B.¹  Don, W. S.²  Abbassi, H.³  Mashayek, F.³ 

[1] San Diego State Univ, Dept Aerosp Engn & Engn Mech, San Diego, CA 92182 USA

[2] Ocean Univ China, Sch Math Sci, Qingdao, Peoples R China

[3] Univ Illinois, Dept Mech & Ind Engn, Chicago, IL 60607 USA

关键词: Discontinuous spectral element;    Artificial viscosity;    Shock sensor;    Adaptive filter;    Viscous compressible flows;    Supersonic cavity flow;   

DOI  :  10.1016/j.jcp.2016.11.042

来源: Elsevier

【 摘 要 】

A spatio-temporal adaptive artificial viscosity (AV) based shock-capturing scheme is proposed for the solution of both inviscid and viscous compressible flows using a high order parallel Discontinuous Spectral Element Method (DSEM). The artificial viscosity and artificial thermal conduction coefficients are proportional to the viscous and thermal entropy generating terms, respectively, in the viscous entropy conservation law. The magnitude of AV is limited based on the explicit stable CFL criterion, so that the stable artificial viscous time step size is greater than the convective stable time step size. To further ensure the stability of this explicit approach, an adaptive variable order exponential filter is applied, if necessary, in elements where the AV has been limited. In viscous flow computations a modified Jameson's sensor (Ducros et al., 1999 [61]) limits the AV to small values in viscous shear regions, so as to maintain a high-order resolution in smooth regions and an essentially non-oscillatory behavior near sharp gradients shocks regions. We have performed a systematic and extensive validation of the algorithm with one-dimensional problems (inviscid moving shock and viscous shock-structure interaction), two-dimensional problems (inviscid steady and unsteady shocked flows and viscous shock boundary layer interaction), and a three-dimensional supersonic turbulent flow over a ramped cavity. These examples demonstrate that the explicit DSEM scheme with adaptive artificial viscosity terms is stable, accurate and efficient. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free