Current Problems in Numerical Analysis

Implicit upwind finite volume methods for incompressible and compressible flows

The talk will discuss an in-house implementation of finite volume method for Navier-Stokes equations with turbulence models, suitable for engineering applications. The choice of elements of the method is motivated by features as sufficient accuracy, suitability for high aspect ratio grids, relatively fast solution, robustness and unified approach in 2D and 3D. It led to implicit upwind discretization on multi-block structured grids. The class of AUSM (upwind) schemes will be discussed. Linearization and solution of the algebraic linear system will be described. Approaches dealing with numerical phenomena as pressure-velocity decoupling and negative pressure (in compressible flow) will be discussed. Some remarks will be given to parallel implementation and in-house tool for grid generation. Examples of incompressible and compressible flow simulations will be presented.