多孔介质流动的中心格式
Central Schemes for Porous Media Flows
AI总结：
本文比较了Kurganov-Tadmor半离散中心格式与Nessyahu-Tadmor中心格式在求解多孔介质多相流双曲守恒律中的表现，发现KT格式扩散更小但在高渗透通道中可能产生错误边界行为。
摘要：
我们关注用于求解非均质多孔介质中多相流模拟产生的标量双曲守恒律的中心差分格式。比较了Kurganov-Tadmor (2000) 半离散中心格式与Nessyahu-Tadmor (1990) 中心格式。KT格式利用关于局部传播速度的更精确信息，并结合包含黎曼扇的非均匀控制体积上的积分。这些方法能够准确解析流体饱和度中的尖锐前沿，而不会引入虚假振荡或过度数值扩散。我们首先讨论了这些方法与由混合有限元近似的速度场的耦合。然后，给出了多尺度非均质石油储层中二维两相流动问题的数值模拟。我们发现KT格式的扩散性明显更小，特别是在存在高渗透流动通道的情况下，这导致了对时间步长选择的严格限制；然而，KT格式可能产生不正确的边界行为。
英文摘要：
We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws arising in the simulation of multiphase flows in heterogeneous porous media. We compare the Kurganov-Tadmor, 2000 semi-discrete central scheme with the Nessyahu-Tadmor, 1990 central scheme. The KT scheme uses more precise information about the local speeds of propagation together with integration over nonuniform control volumes, which contain the Riemann fans. These methods can accurately resolve sharp fronts in the fluid saturations without introducing spurious oscillations or excessive numerical diffusion. We first discuss the coupling of these methods with velocity fields approximated by mixed finite elements. Then, numerical simulations are presented for two-phase, two-dimensional flow problems in multi-scale heterogeneous petroleum reservoirs. We find the KT scheme to be considerably less diffusive, particularly in the presence of high permeability flow channels, which lead to strong restrictions on the time step selection; however, the KT scheme may produce incorrect boundary behavior.
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