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

Autor:	Tveit, Jesper
Rok vydání:	2014
Předmět:	Physics - Computational Physics Physics - Fluid Dynamics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 19 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1409.1072 Zobrazit plný text záznamu View this record from Arxiv