THE OGRE CODE: A TWO-DIMENSIONAL NUMERICAL MODEL OF THE TRANSIENT FLOW OF ONE OR TWO COMPRESSIBLE FLUIDS THROUGH CONFINED POROUS MEDIA.

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

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Interface stability of compressible fluids in porous media

Physics of Fluids ◽

10.1063/5.0059336 ◽

2021 ◽

Vol 33 (8) ◽

pp. 084102

Author(s):

Thi Thai Le ◽

Thorsten Koch

Keyword(s):

Porous Media ◽

Compressible Fluids ◽

Interface Stability

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Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

Applied Sciences ◽

10.3390/app11083421 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3421

Author(s):

Cheng-Yu Ku ◽

Li-Dan Hong ◽

Chih-Yu Liu ◽

Jing-En Xiao ◽

Wei-Po Huang

Keyword(s):

Porous Media ◽

Time Domain ◽

Numerical Solutions ◽

Space Time ◽

Two Dimensional ◽

Transient Flows ◽

Layered Porous Media ◽

Time Marching ◽

Time Basis ◽

Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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