Abstract

A new dynamic verification of the one-dimensional (1-D) computational Two-Fluid Model (TFM) using the Type II density wave instability (DWI) theory of Ishii is presented. Verification requires convergence in the sense of the Lax Equivalence Theorem and dynamic comparison with the DWI theory. Rigorous verification of the computational TFM must be performed with a computational model that is well posed without regularization because, otherwise, since the theory of Ishii is well posed, regularization would make the TFM incompatible with it.

Furthermore, since the TFM is well posed, it was possible to implement a second-order numerical method with a flux limiter that, together with a fine mesh, achieves numerical convergence. This is significant because numerical convergence and consistency, both of which are demonstrated, are prerequisites for the rigorous dynamic verification according to the Lax Equivalence Theorem. Thus, the apparent but previously unproven numerical verification of the 1-D TFM to simulate the two-phase long wave DWI instability is hereby performed.

摘要

介绍了使用 Ishii 的 II 型密度波不稳定性 (DWI) 理论对一维 (1-D) 计算二维流体模型 (TFM) 进行的新动态验证。验证需要 Lax 等价定理意义上的收敛以及与 DWI 理论的动态比较。计算 TFM 的严格验证必须使用没有正则化的良定计算模型来执行，否则，由于 Ishii 的理论是良定的，正则化会使 TFM 与其不兼容。

此外，由于 TFM 是适定的，因此可以使用通量限制器实现二阶数值方法，该方法与精细网格一起实现数值收敛。这很重要，因为数值收敛和一致性，这两者都得到证明，是根据松散等价定理进行严格动态验证的先决条件。因此，特此执行对一维 TFM 进行明显但先前未经证实的数值验证，以模拟两相长波 DWI 不稳定性。