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Hypersonic flow. --- Computational fluid dynamics. --- Navier-Stokes equation. --- Data transmission. --- Reaction kinetics. --- Flow distribution.

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Transonic compressors. --- Pressure distribution. --- Large eddy simulation. --- Navier-Stokes equation. --- Computational fluid dynamics. --- Flow characteristics. --- Reynolds averaging. --- Separated flow. --- Turbulent flow. --- Boundary layer separation.

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Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux. As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.

Navier-Stokes equations. --- Thermodynamics. --- Viscous flow. --- Viscous flow --- Thermodynamics --- Navier-Stokes equations --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Equations, Navier-Stokes --- Physics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Continuum physics. --- Classical Continuum Physics. --- Partial Differential Equations. --- Analysis. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Partial differential equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Fluid dynamics --- Viscosity --- Differential equations, Partial --- Differential equations, partial. --- Global analysis (Mathematics). --- Classical and Continuum Physics. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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The monograph is devoted to modern mathematical models and numerical methods for solving gas- and fluid-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 coefficient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective finite-difference algorithms for calculating viscous non-stationary flows are constructed and examples of numerical computations are presented. The universality, the efficiency, and the exactness of the algorithms constructed are ensured by the fulfillment 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 fluid flows and also for students and post-graduated students who specialize in numerical gas and liquid dynamics.

Fluid dynamics -- Mathematical models. --- Gas dynamics -- Mathematical models. --- Gas dynamics --- Fluid dynamics --- Applied Mathematics --- Engineering & Applied Sciences --- Mathematical models --- Fluid dynamics. --- Gas dynamics. --- Navier-Stokes equations --- Numerical solutions. --- Gasdynamics --- Engineering. --- Computer mathematics. --- Fluids. --- Fluid mechanics. --- Engineering Fluid Dynamics. --- Fluid- and Aerodynamics. --- Computational Science and Engineering. --- Numerical analysis --- Thermodynamics --- Dynamics --- Fluid mechanics --- Hydraulic engineering. --- Computer science. --- Informatics --- Science --- Engineering, Hydraulic --- Engineering --- Hydraulics --- Shore protection --- Computer mathematics --- Electronic data processing --- Mathematics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Hydromechanics --- Continuum mechanics