We have developed a new discontinuous Galerkin (DG) method to solve the 2D seismic wave equations in isotropic and anisotropic media. This method uses a modified numerical flux that is based on a linear combination of the Godunov and the centered fluxes. A weighting factor is introduced in this modified numerical flux that is expected to be optimized to some extent. Through the investigations on the considerations of numerical stability, numerical dispersion, and dissipation errors, we develop a possible choice of optimal weighting factor. Several numerical experiments confirm the effectiveness of the proposed method. We evaluate a convergence test based on cosine wave propagation without the source term, which shows that the numerical errors in the modified flux-based DG method and the Godunov-flux-based method are quite similar. However, the improved computational efficiency of the modified flux over the Godunov flux can be demonstrated only at a small sampling rate. Then, we apply the proposed method to simulate the wavefields in acoustic, elastic, and anisotropic media. The numerical results show that the modified DG method produces small numerical dispersion and obtains results in good agreement with the reference solutions. Numerical wavefield simulations of the Marmousi model show that the proposed method also is suitable for the heterogeneous case.

中文翻译：

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在二维和各向异性介质中二维波传播的基于数值通量的改进非连续Galerkin方法

我们已经开发了一种新的不连续伽勒金（DG）方法来求解各向同性和各向异性介质中的二维地震波方程。此方法使用基于Godunov和居中通量的线性组合的改进数值通量。在此修改的数值通量中引入了一个加权因子，该加权因子有望在某种程度上进行优化。通过对数值稳定性，数值色散和耗散误差的考虑，我们找到了最佳加权因子的可能选择。几个数值实验证实了该方法的有效性。我们评估了基于余弦波传播而没有源项的收敛测试，这表明改进的基于通量的DG方法和基于Godunov-通量的方法中的数值误差非常相似。然而，改进的通量比Godunov通量提高的计算效率只能在很小的采样率下得到证明。然后，我们将所提出的方法应用于模拟声，弹性和各向异性介质中的波场。数值结果表明，改进的DG方法数值离散较小，与参考解的计算结果吻合良好。Marmousi模型的波场数值模拟表明，该方法也适用于非均质情况。数值结果表明，改进的DG方法数值离散较小，与参考解的计算结果吻合良好。Marmousi模型的波场数值模拟表明，该方法也适用于非均质情况。数值结果表明，改进的DG方法产生的数值离散较小，并且获得的结果与参考解具有很好的一致性。Marmousi模型的波场数值模拟表明，该方法也适用于非均质情况。