A spectral method for the triangular cavity flow

• Published in: Computers & fluids 2014-05, Vol.95, p.40-48
• Main Authors: Jagannathan, Arjun, Mohan, Ranjith, Dhanak, Manhar
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Computer simulation; Coordinate mapping; Fluid flow; Influence matrix method; Lid driven cavity; Mathematical analysis; Mathematical models; Navier-Stokes equations; Spectral collocation; Unsteady; Walls
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2014.02.003

•We perform the first spectral simulations for the triangular cavity flow.•Chebyshev collocation method in triangular domain using singular mapping.•Singularity subtraction at top corners of the flow.•Finite difference preconditioning for Laplacian and Helmholtz operators.•Detailed flow characteristics for Reynolds number 100, 500 and 1000. We describe the use of a spectral collocation method to compute the characteristics of incompressible, viscous flow in a lid driven right triangular cavity with wall motion away from the right angle. First, the 2-D Gauss–Lobatto grid on the square [-1,1]×[-1,1] is mapped to a triangular domain by means of a singular mapping. A singularity subtraction technique is used to account for the most singular terms of the asymptotic expansions near the top corners of the flow. The unsteady Navier–Stokes equations in the vorticity–streamfunction formulation are then solved in this transformed grid using an influence matrix technique. A third order Adams Bashforth/Backward differentiation method appears to provide excellent numerical stability for the scheme and also permits a larger critical time step. Detailed characteristics of the flow and comparisons with published results are presented.