Finite Volume Discretization of the Three Dimensional Incompressible Navier-Stokes Equation in General Coordinates

摘要

In the report the authors study the discretization of the incompressible Navier-Stokes equations in general coordinates by means of finite volume integration. Three types of discretization are compared using as unknowns covariant and contravariant velocity components and contravariant flux components, respectively. All three discretizations will be derived from the discretization of the Navier-Stokes equations in vector form by taking the inner product of the latter with properly chosen constant vector fields.