Residual distribution for general time-dependent conservation laws

  • Authors:

  • Mario Ricchiuto;Árpád Csík;Herman Deconinck

  • Affiliations:

  • von Karman Institute for Fluid Dynamics, Department of Aeronautics and Aerospace, 72 Chaussée de Waterloo, B-1640 Rhode-Saint-Genèse, Belgium;Katholieke Universiteit Leuven, Department of Mathematics, Center for Plasma-Astrophysics, Leuven Celestijnenlaan 200B, B3000 Belgium;von Karman Institute for Fluid Dynamics, Department of Aeronautics and Aerospace, 72 Chaussée de Waterloo, B-1640 Rhode-Saint-Genèse, Belgium

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

Quantified Score

Hi-index 31.50

Visualization

Abstract

We consider the second-order accurate numerical solution of general time-dependent hyperbolic conservation laws over unstructured grids in the framework of the Residual Distribution method. In order to achieve full conservation of the linear, monotone and first-order space-time schemes of (Csik et al., 2003) and (Abgrall et al., 2000), we extend the conservative residual distribution (CRD) formulation of (Csik et al., 2002) to prismatic space-time elements. We then study the design of second-order accurate and monotone schemes via the nonlinear mapping of the local residuals of linear monotone schemes. We derive sufficient and necessary conditions for the well-posedness of the mapping. We prove that the schemes obtained with the CRD formulation satisfy these conditions by construction. Thus the nonlinear schemes proposed in this paper are always well defined. The performance of the linear and nonlinear schemes are evaluated on a series of test problems involving the solution of the Euler equations and of a two-phase flow model. We consider the resolution of strong shocks and complex interacting flow structures. The results demonstrate the robustness, accuracy and non-oscillatory character of the proposed schemes. d schemes.