A Taylor Weak Statement CFD Algorithm for Free Surface Hydromechanical Flows - Baker, A.J.; Iannelli, G.S. (Developments in Water Science, 1988)
A finite element CFD algorithm is established for the two-dimensional, unsteady depth-averaged free surface Navier-Stokes equations for an incompressible isoenergetic flow. The governing equation set is cast in hyperbolic conservation law form, whereupon a temporal Taylor series is utilized to establish truncation error terms. The resulting Taylor weak statement embeds functional expressions dominating dispersion and dissipation error mechanisms of the semi-discrete approximation. Theoretical analyses are developed to characterize these mechanisms for the linear basis implementation. An efficient numerical linear algebra procedure is developed using matrix tensor products. Numerical results are highlighted that document algorithm performance.