On The Navier‐Stokes Equations with Constant Total Temperature

Abstract

For various applications in fluid dynamics, one can assume that the total temperature is constant. Therefore, the energy equations can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed in this paper. It is shown that the system is strictly hyperbolic and well posed for the initial‐value problem. Boundary conditions are described such that the linearized system is well posed. The hopscotch method is investigated and numerical results are presented.

Computation of flow around wings based on the Euler equations

“…Since we work only with their First Approximation, it is easier to grasp the idea if we present our boundary condition in a heuristic development based directly on the characteristic variables instead of the formal theory. The presentation for our 4 x 4 system mirrors the one given by Gottlieb & Gustafsson (1976) for the 3 x 3 system, but is more general because of our non-orthogonal coordinates.…”

Simulation of time-dependent compressible viscous flows using central and upwind-biased finite-difference techniques

“…Viscous terms are evaluated using the latest updated values of the dependent variables, thus introducing an effective lag ging to avoid compromising the linearity of the equations. The overall time accuracy of the method is not impaired by this treatment; however, it is pointed out in [79] that an additional dissipative truncation error term is generated. Metric derivatives are also centrally differenced to satisfy the grid conservation law [58].…”

“…This approach is computation ally explicit, efficient, easily programmable, has minimal storage requirements, and posseses optimal pseudo-viscosity damping charateristics. Gottlieb and Gustaffson[79] presented a modified hopscotch approach including a special linearization for diffusion terms which maintained the overall explicit nature of the algorithm.…”