|Title||A spectral method for the triangular cavity flow|
|Publication Type||Journal Article|
|Year of Publication||2014|
|Authors||Jagannathan A., Mohan R., Dhanak M.|
|Journal||Computers & Fluids|
|Type of Article||Article|
|Keywords||Coordinate mapping; driven cavity; efficient numerical techniques; equations; Influence; Lid driven cavity; matrix method; navier-stokes; Spectral collocation; steady viscous-flow|
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] x [-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-stream function 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. (C) 2014 Elsevier Ltd. All rights reserved.