A Numerical Approach to Solving Nonlinear Differential Equations on a Grid with Potential Applicability to Computational Fluid Dynamics

摘要

A finite element method for solving nonlinear differential equations on agrid, with potential applicability to computational fluid dynamics (CFD), isdeveloped and tested. The current method facilitates the computation ofsolutions of a high polynomial degree on a grid. A high polynomial degree isachieved by interpolating both the value, and the value of the derivatives upto a given order, of continuously distributed unknown variables. Thetwo-dimensional lid-driven cavity, a common benchmark problem for CFD methods,is used as a test case. It is shown that increasing the polynomial degree hassome advantages, compared to increasing the number of grid-points, when solvingthe given benchmark problem using the current method. The current method yieldsresults which agree well with previously published results for this test case.