Research on numerical algorithms for the threedemensional NavierStokes equations. 2: Dissipative finite element
Abstract
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 multidimensional 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 NavierStokes solution algorithm.
 Publication:

Interim Technical Report
 Pub Date:
 February 1981
 Bibcode:
 1981tenn.reptS....B
 Keywords:

 Finite Element Method;
 NavierStokes Equation;
 Three Dimensional Flow;
 Aerodynamics;
 Flow Distribution;
 Kinematics;
 Numerical Analysis;
 Fluid Mechanics and Heat Transfer