A cartesian compact scheme for the Navier-Stokes equations in streamfunction formulation in irregular domains

Matania Ben-Artzi (1) , Jean-Pierre Croisille (2) , Dalia Fishelov (3)

1 HUJ - The Hebrew University of Jerusalem
2 IECL - Institut Élie Cartan de Lorraine
3 AFEKA - The Academic College of Engineering in Tel Aviv

In [3] we introduced an embedded Cartesian scheme for the biharmonic problem in two dimensions. Here we extend this methodology to the 2D Navier-Stokes system. Hermite (or Birkhoff) interpolation is invoked in one and two dimensions to obtain finite difference operators. The consistency analysis of the discrete formulas for irregular grids is emphasized. Numerical results demonstrate remarkable accuracy for a series of test cases for flows in elliptical domains.

Mots clés: Biharmonic problem; embedded compact scheme; Navier-Stokes equations

Domaines: Mathématiques [math]

Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov. A cartesian compact scheme for the Navier-Stokes equations in streamfunction formulation in irregular domains. Journal of Scientific Computing, 2019, 81 (3), pp.1386-1408. ⟨10.1007/s10915-019-01012-2⟩. ⟨hal-03264806⟩