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A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics

Boscheri, W. ; Dumbser, M. ; Ioriatti, M. ; Peshkov, I. ; Romenski, E.

Journal of computational physics, 2021-01, Vol.424, p.109866, Article 109866 [Periódico revisado por pares]

Cambridge: Elsevier Inc

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  • Título:
    A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics
  • Autor: Boscheri, W. ; Dumbser, M. ; Ioriatti, M. ; Peshkov, I. ; Romenski, E.
  • Assuntos: Asymptotic preserving schemes ; Asymptotic properties ; Compressibility ; Computational fluid and solid mechanics ; Computational fluid dynamics ; Conducting fluids ; Continuum mechanics ; Discretization ; Finite volume method ; Fluid flow ; Heat transmission ; Mach number ; Mathematical models ; Navier-Stokes equations ; Pressure-based all Mach number flow solver ; Staggered semi-implicit finite volume schemes ; Strain ; Structure-preserving curl-free schemes ; Symmetric hyperbolic and thermodynamically compatible systems (SHTC)
  • É parte de: Journal of computational physics, 2021-01, Vol.424, p.109866, Article 109866
  • Descrição: We propose a new pressure-based structure-preserving (SP) and quasi asymptotic preserving (AP) staggered semi-implicit finite volume scheme for the unified first order hyperbolic formulation of continuum mechanics [1], which goes back to the pioneering work of Godunov [2] and further work of Godunov & Romenski [3] and Peshkov & Romenski [4]. The unified model is based on the theory of symmetric-hyperbolic and thermodynamically compatible (SHTC) systems [2,5] and includes the description of elastic and elasto-plastic solids in the nonlinear large-strain regime as well as viscous and inviscid heat-conducting fluids, which correspond to the stiff relaxation limit of the model. In the absence of relaxation source terms, the homogeneous PDE system is endowed with two stationary linear differential constraints (involutions), which require the curl of distortion field and the curl of the thermal impulse to be zero for all times. In the stiff relaxation limit, the unified model tends asymptotically to the compressible Navier-Stokes equations. The new structure-preserving scheme presented in this paper can be proven to be exactly curl-free for the homogeneous part of the PDE system, i.e. in the absence of relaxation source terms. We furthermore prove that the scheme is quasi asymptotic preserving in the stiff relaxation limit, in the sense that the numerical scheme reduces to a consistent second order accurate discretization of the compressible Navier-Stokes equations when the relaxation times tend to zero. Last but not least, the proposed scheme is suitable for the simulation of all Mach number flows thanks to its conservative formulation and the implicit discretization of the pressure terms. •New semi-implicit structure preserving finite volume scheme for continuum mechanics.•Vertex-based staggering of the thermal impulse J and the distortion field A.•The method is exactly curl-free on the discrete level for A and J in the absence of source terms.•The method is quasi asymptotic preserving for the viscous stress tensor and the heat flux.•The method is pressure based and suitable for the simulation of low Mach number flows.
  • Editor: Cambridge: Elsevier Inc
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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