The space–time CE/SE method for solving single and two-phase shallow flow models

• The single-phase and two-phase shallow flow models are numerically investigated.
• The space–time CE/SE method is applied to solve these models.
• For comparison the KFVS scheme is used.
• Both schemes are applied for the first time to two-phase shallow flow models.
• Numerical results verify the accuracy and robustness of the proposed schemes.

In this paper, the space–time conservation element and solution element (CE/SE) method is applied for simulating single-phase and two-phase shallow flows with bottom topography. The single-phase shallow water equations contain the flow height, momentum and the flow velocity. The two-phase flow is considered as a shallow layer of solid granular material and fluid over a horizontal surface. The solid and fluid components are assumed to be incompressible. The flow height, solid volume fraction and phase momenta are also considered. The latter equations contain source terms for accounting the inter-phase drag forces. Our primary interest is the numerical approximation of aforementioned solid–fluid model, whose complexity poses numerical difficulties. The proposed numerical method differs from the previous techniques because of global and local flux conservation in a space–time domain without restoring to interpolation and extrapolation. In order to reveal the efficiency and performance of the approach, several numerical test cases are carried out. For validation, the results of suggested method are compared with the KFVS method.