Investigation of an economical finite difference scheme for an unsteady viscous weakly compressible gas flow

An implicit finite difference scheme with a splitting operator is constructed for a linear system of equations describing an unsteady viscous weakly compressible gas flow in the case of two spatial variables. The use of a splitting operator made it possible to propose an algorithm for seeking a difference solution in explicit form by the Fourier method. For the numerical solution obtained with this scheme, an error estimate is proved depending on the parameter characterizing the gas compressibility and gas viscosity. The numerical results presented show the efficiency of this method in comparison with an implicit scheme based on iterative conjugate gradient methods.