TABLE OF CONTENTS Problems posed by high-speed gas flow are of obvious practical importance. Applications range from the exterior flows associated with flight to interior flows typical of turbomachinery. As the cost of physical experiments is high, the possibilities of computations were explored early and the development concentrated on the use of finite difference methods. It was only in the 1980s that the potential offered by the finite element forms were realized.
One of the main advantages in the use of the finite element approximation here is its capability of fitting complex forms and permitting local refinement where required. However, the improved accuracy attainable by finite element methods is also of substantial importance as practical problems will often involve three-dimensional discretization with a very large number of degrees of freedom much larger than those encountered in typical structural problems.
For such large problems direct solution methods are obviously not practicable and iterative methods based generally on transient computation forms are invariably used. Here of course we follow and accept much that has been established by the finite difference applications but generally will lose some computational efficiency associated with structured meshes. However, the reduction of the problem size which, as we shall see, can be obtained by local refinement and adaptivity will more than compensate for this loss (though of course structured meshes are included in the finite element forms).
In Chapters 1 and 3 we have introduced the basic equations governing the flow of compressible gases as well...
