Tracking a sharp crested wave front in hyperbolic heat transfer |
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Authors: | RH Sieberhagen NFJ van Rensburg |
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Institution: | Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa |
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Abstract: | In this article we investigate the numerical oscillations encountered when approximating the solution to the hyperbolic heat conduction equation. We consider a benchmark problem and show that it is not well-posed, unless a jump condition is specified. The alternative is to “smooth” the jump which leads to a sharp crested wave front, but with no discontinuity. To track the wave front we split the problem into auxiliary problems and solve these using different methods. The resulting solution is oscillation-free. |
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Keywords: | Hyperbolic heat conduction Finite element method Numerical oscillations Jump condition |
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