The monograph is devoted to modern mathematical models and numerical methods for solving gas- and ?uid-dynamic problems based on them. Two interconnected mathematical models generalizing the Navier Stokes system are presented; they differ from the Navier Stokes system by additional dissipative terms with a small parameter as a coef?cient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective ?nite-difference algorithms for calculating viscous nonstationary ?ows are constructed and examples of numerical computations are presented....