Characteristic-based finite volume scheme for 1D Euler equations |
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Authors: | Yan Guo Ru-xun Liu |
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Institution: | (1) Department of Mathematics, University of Science and Technology of China, Hefei, 230026, P. R. China |
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Abstract: | In this paper, a high-order finite-volume scheme is presented for the onedimensional scalar and inviscid Euler conservation
laws. The Simpson’s quadrature rule is used to achieve high-order accuracy in time. To get the point value of the Simpson,s
quadrature, the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the
characteristic curves, and the third-order and fifth-order central weighted essentially non-oscillatory (CWENO) reconstruction
is adopted to estimate the cell point values. Several standard one-dimensional examples are used to verify the high-order
accuracy, convergence and capability of capturing shock.
Project supported by the National Natural Science Foundation of China (No. 10771134) |
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Keywords: | hyperbolic equation finite volume method characteristic theory WENO reconstruction Runge-Kutta method |
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