An efficient LU-TVD finite volume method for 3D inviscid and viscous incompressible flow problems

This Duper presents the application of an upwind TVD scheme to a flow described by the pseudo-compressible formulation of the 3D Euler and Navier-Stokes equations. Firstly, the mathematical formulation of the problem is presented. This includes a discussion of the governing equations and their transformation. Secondly, the discretization by implicit finite volume method is used, Finally, the resulting third-order accurate scheme is then solved by the economical LU-decomposition method, which requires only one forward and one backward sweeps with the scalar diagonal inversions. The solver developed on the base of present method is then used to calculate the flaw around SIB-NIA S-16 airfoil, the 3D laminar flows through both a square and a circular duct with 90 degrees bend, 3D inviscid flows through the Francis and Kaplan turbine runners and in straight-flow needle nozzle of the Pelton turbine. Comparisons with the experimental data and other numerical solutions showed Hood agreements.