Shock-capturing method using characteristic-based dissipation filters in pressure-based algorithm

• Published in: Acta mechanica Vol. 209; no. 1-2; pp. 99 - 113
• Main Authors: Djavareshkian, M. H., Abdollahi Jahdi, M. H.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 2010; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Classical and Continuum Physics; Compressible flows; shock and detonation phenomena; Control; Criteria; Dynamical Systems; Engineering; Engineering Thermodynamics; Eulers equations; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Mechanical engineering; Methods; Physics; Pressure; Shock-wave interactions and shock effects; Solid Mechanics; Supersonic and hypersonic flows; Theoretical and Applied Mechanics; Vibration; Contact Discontinuity; Total Variation Diminish; Mach Number; Residual History; Total Variation Diminish Scheme; Supersonic flow; Method of characteristics; Discontinuity; Transonic flow; Adhesive wear; Flow rate; Steady flow; Euler equations; Steady state; Finite volume methods; Shock waves; Filters; Non viscous fluid; Convergence rate; Modelling
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-009-0144-9

In this paper, an efficient blending procedure based on the pressure-based algorithm is presented to solve the compressible Euler equations on a non-orthogonal mesh with collocated finite volume formulation. The boundedness criteria for this procedure are determined from total variation diminishing (TVD) schemes with and without applying of artificial compression method (ACM) of Harten as a control switch of dissipation. The fluxes of the convected quantities including mass flow rate are approximated by using the characteristic-based TVD and TVD/ACM methods. The algorithm is tested for steady-state inviscid flows at different Mach numbers ranging from the transonic to the supersonic regime and the results are compared with the existing numerical solutions. The comparisons show that the ACM is a useful technique to modify standard high-resolution schemes, which prevents the smearing of discontinuities and improves the resolution of shocks in the pressure-based algorithm. Aside from having the ability of accurately capturing shocked flows, this approach also accelerates the convergence rate of the solution in the supersonic flows with only a maximum increase of 5% in the operations with respect to standard second-order TVD schemes.