Research on numerical algorithms for the three-demensional Navier-Stokes equations. 2: Dissipative finite element

The objective of this research project is to derive and evaluate versatile, accurate and efficient numerical algorithms for solution of aerodynamic flowfields at large Reynolds number. The concept of a dissipative finite element algorithm has been refined and extended to solution of a complete equation set in aerodynamics. The resultant numerical results are highly encouraging with respect to shock resolution and overall performance, utilizing both a linear quadratic finite element embodiment of the theory. The theoretical formulational statement of the algorithm has been extended to a multi-dimensional description in generalized coordinates. The key efficiency feature is identification of the tensor matrix resolution of the Jacobian of the Newton algorithm for this statement. The concept of application of the continuity equation solution, as a differential constraint on the momentum equation algorithm, has been validated. The formulation is directly useful for viscous marching procedures, and with some modifications could be equally useful for a low Mach number Navier-Stokes solution algorithm.