Application of splitting algorithms to the finite volume method (Q2729346)

The author constructs finite difference schemes based on the use of finite volume method for numerical solution of Euler equations for compressible gases and incompressible fluids. The author notes that schemes of this type can be applied to numerical study of Navier-Stokes equations for a compressible heat conducting gas. The so-called viscosity terms in Navier-Stokes equations can be approximated at fractional steps by convective terms. The algorithms are constructed on regular meshes. It is also shown that algorithms which use the splitting of the corresponding operators into physical processes can be applied to numerical solution of Euler and Navier-Stokes equations on regular nonstaggered meshes; their numerical realization is reduced to solutions of the equations for velocity and pressure components. These economical algorithms are characterized by minimum dissipation properties; moreover, the algorithms can be used on multiprocessor computers.