AN ADAPTIVE SECOND-ORDER PROJECTION METHOD FOR UNSTEADY FLOWS
Millena M. Villar1; Alexandre M. Roma2; Aristeu da Silveira Neto1; Hector D. Ceniceros3
1 Universidade Federal de Uberlândia; 2 Universidade de S~ao Paulo; 3 University of California
Resumo
A new methodology based on projection method which allow to simulate incompressible flows is presented in this work. The integration domain is discretized on a block-structured adaptive mesh. This approach consist on a sequence of nested grids with successively finer spacing with refinement ratio equal to 2. This new implementation of projection method is based on Gear method where the forcing term is extrapolated in two time-steps assuring second-order to the velocities (O(dt2, dx2)) but at least first-order to the pressure and CFL condition to the time-step constraint. The multigridmultilevel method is applied to advection-diffusion equation and to the Poisson equation solution of pressure correction, both of which are spatially discretized with second-order centered finite differences method. The turbulent viscosity proposed by Smagorisnky which is a linear model is introduced in an explicit time way. The method is checked trough some examples where the fluid properties might be constant or variable and the integration meshes might be as well as not be locally refined.
Palavras-chave: Adaptive mesh; Gear method; Projection method