Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws
Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws
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DOI：
10.1016/j.jcp.2011.08.024
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发表时间：
2011-10
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影响因子：
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通讯作者：
Khosro Shahbazi;Nathan Albin;O. Bruno;J. Hesthaven
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文献类型：
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作者：
Khosro Shahbazi;Nathan Albin;O. Bruno;J. Hesthaven
本文介绍了一种多区域傅立叶延拓/WENO混合方法(FC-WENO)，它能够实现非线性守恒律组的高阶非振动解，并且具有基本无色散、远离间断的谱特征以及温和的CFL约束(与有限差分方法相当)。混合格式在包含间断的小区域使用昂贵的捕捉激波的WENO方法，在计算区域的其余部分使用高效的FC方法，从而为具有间断和复杂光滑结构的应用产生了一个高效的整体格式。用Harten的多分辨程序区分了光滑和不连续的解区域[J.Comput]。太棒了。115(1994)319-338]。我们考虑五阶和九阶的WENO格式和五阶的FC方法。对具有光滑解和非光滑解的守恒律问题，研究了新混合方法的精度、稳定性和效率。在后一种情况下，我们求解了马赫数为3的激波与熵波相互作用，以及激波(马赫数为1.25、3或6)与极小的熵波相互作用的标准试验情形下的气体动力学欧拉方程，并与纯WENO方法和其他基于混合方法的方法进行了比较，评价了混合FC-WENO方法的有效性。我们展示了新的基于FC的方法的相当大的计算优势，当扩展到完全三维问题时，表明比其他方法有一个数量级的加速潜力。
We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC–WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319–338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC–WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems.