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arXiv · 1409.1072

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

Jesper Tveit
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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.

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Jesper Tveit. 2014-09-03. A Numerical Approach to Solving Nonlinear Differential Equations on a Grid with Potential Applicability to Computational Fluid Dynamics. https://arxiv.org/abs/1409.1072

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