Application of the fictitious domains method for the simulation of gas flows at low Mach numbers

A new approach to the simulation of slightly-compressible gas flows based on the quasigasdynamic system of equations is under consideration. The procedure of pressure decomposition into two components — a volume-averaged part and a dynamic part - is proposed. To derive the dimensionless form of the equations, different reference values for these components are used what allows to avoid singularities at Mach number tending to zero. A special computational algorithm including the solution of elliptic equation for the increment of the pressure dynamic component is developed. To ensure homogeneity of the algorithm, the fictitious domain method is used. Test predictions indicate accuracy and robustness of the proposed methods.