High-order monotonicity-preserving compact schemes for linear scalar advection on 2-D irregular meshes

  • Authors:

  • Quang Huy Tran;Bruno Scheurer

  • Affiliations:

  • Institut Français du Pétrole, Division Informatique Scientifique et Mathématiques Appliquées, 1 et 4 avenue de Bois Préau, 92852 Rueil-Malmaison Cedex, France;Commissariat à l' Energie Atomique, DIF, B.P. 12, 91680 Bruyéresle-Châtel, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

This paper is concerned with the numerical solution for linear scalar advection problems, the velocity field of which may be uniform or a given function of the space variable. We would like to propose the following: (1) a new family of 1-D compact explicit schemes, which preserve monotonicity while maintaining high-order accuracy in smooth regions; and (2) an extension to the 2-D case of this family of schemes, which ensures good accuracy and isotropy of the computed solution even for very distorted meshes. A few theoretical results are proven, while abundant numerical tests are shown in order to illustrate the quality of the schemes at issue.