A Numerical Approach to Solving Nonlinear Differential Equations on a Grid with Potential Applicability to Computational Fluid Dynamics
Abstract
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a high polynomial degree on a grid. A high polynomial degree is achieved by interpolating both the value, and the value of the derivatives up to a given order, of continuously distributed unknown variables. The two-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 has some advantages, compared to increasing the number of grid-points, when solving the given benchmark problem using the current method. The current method yields results which agree well with previously published results for this test case.
Cite
@article{arxiv.1409.1072,
title = {A Numerical Approach to Solving Nonlinear Differential Equations on a Grid with Potential Applicability to Computational Fluid Dynamics},
author = {Jesper Tveit},
journal= {arXiv preprint arXiv:1409.1072},
year = {2014}
}
Comments
19 pages, 8 figures