This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.

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 NavierStokes system are presented; they differ from the NavierStokes 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. The universality, the ef?ciency, and the exactness of the algorithms constructed are ensured by the ful?llment of integral conservation laws and the theorem on entropy balance for them. The book is a course of lectures and is intended for scientists and engineers who deal with constructing numerical algorithms and performing practical calculations of gas and ?uid ?ows and also for students and postgraduate students who specialize in numerical gas and ?uid dynamics.

Presents new models for solving gas- and fluid-dynamic problems Shows many examples of numerical computations Includes supplementary material: sn.pub/extras

Inhalt
Construction of Gas-Dynamic Equations by Using Conservation Laws.- Elements of Kinetic Gas Theory.- Quasi-gas-dynamic Equations.- Quasi-gas-dynamic Equations and Coordinate Systems.- Numerical Algorithms for Solving Gas-Dynamic Problems.- Algorithms for Solving the Quasi-gas-dynamic Equations on Nonstructured Grids.- Quasi-hydrodynamic Equations and Flows of Viscous Incompressible Fluids.- Quasi-gas-dynamic Equations for Nonequilibrium Gas Flows.- Quasi-gas-dynamic Equations for Binary Gas Mixtures.