Partial differential equations computational fluid mechanics

E.J. Kansa. Multiquadratics- a scattered data approximation scheme with applications to computational fluid mechanics, ii-solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers Math. Applic., 19 147, 1990. 

The Navier-Stokes equations express the conservation of momentum. Together with the continuity equation, which expresses conservation of mass, these equations are the fundamental underpinning of fluid mechanics. They are nonlinear partial differential equations that in general cannot be solved by analytical means. Nevertheless, there are a number of geometries and flow situations that permit considerable simplification and solution. We will explore many of these and their solution, usually by computational techniques. While... 

Applied Mathematics Branch of mathematics devoted to developing and applying mathematical methods, including math-modeling techniques, to solve scientific, engineering, industrial, and social problems. Areas of focus include ordinary and partial differential equations, statistics, probability, operational analysis, optimization theory, solid mechanics, fluid mechanics, numerical analysis, and scientific computing. 

The establishment of a detailed kinetic model provides an opportunity for the numerical prediction of the behaviour of a chemical system under conditions that may not be accessible by experimental means. However, large-scale models with many variables may require considerable computer resource for their implementation, especially under non-isothermal conditions, for which stiffness of the system of differential equations for mass and energy to be integrated is a problem. Computation in a spatial domain, for which partial differential expressions are appropriate, becomes considerably more demanding. There are also many important fluid mechanical problems in reactive systems, the detailed kinetic representation of the chemistry for which would be highly desirable, but cannot yet be computed economically. In such circumstances there is a place for the use of reduced or simplified kinetic models, as discussed in Chapter 7. Thus,... 

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