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A computational platform for direct numerical simulation of fluid-particle two-phase flow in porous media is presented in this study. In the proposed platform, the Navier-Stokes equations are used to describe the motion of the continuous phase, while the discrete element method (DEM) is employed to evaluate particle-particle and particle-wall interactions, with a fictitious domain method being adopted to evaluate particle-fluid interactions. Particle-wall contact states are detected by the ERIGID scheme. Moreover, a new scheme, namely, base point-increment method is developed to improve the accuracy of particle tracking in porous media. In order to improve computationally efficiency, a time splitting strategy is applied to couple the fluid and DEM solvers, allowing different time steps to be used which are adaptively determined according to the stability conditions of each solver. The proposed platform is applied to particle transport in a porous medium with its pore structure being reconstructed from micro-CT scans from a real rock. By incorporating the effect of pore structure which has a comparable size to the particles, numerical results reveal a number of distinct microscopic flow mechanisms and the corresponding macroscopic characteristics. The time evolution of the inlet to outlet pressure-difference consists of large-scale spikes and small-scale fluctuations. Apart from the influence through direct contacts between particles, the motion of a particle can also be affected by particles without contact through blocking a nearby passage for fluid flow. Particle size has a profound influence on the macroscopic motion behavior of particles. Small particles are easier to move along the main stream and less dispersive in the direction perpendicular to the flow than large particles.

Fictitious domain method (FDM) is a commonly accepted direct numerical simulation technique for moving boundary problems. Indicator function used to distinguish the solid zone and the fluid zone is an essential part concerning the whole prediction accuracy of FDM. In this work, a new indicator function through volume intersection is developed for FDM. In this method, the arbitrarily polyhedral cells across the interface between fluid and solid are located and subdivided into tetrahedrons. The fraction of the solid volume in each cell is accurately computed to achieve high precision of integration calculation in the particle domain, improving the accuracy of the whole method. The quadrature over the solid domain shows that the newly developed indicator function can provide results with high accuracy for variable integration in both stationary and moving boundary problems. Several numerical tests, including flow around a circular cylinder, a single sphere in a creeping shear flow, settlement of a circular particle in a closed container, and in-line oscillation of a circular cylinder, have been performed. The results show good accuracy and feasibility in dealing with the stationary boundary problem as well as the moving boundary problem. This method is accurate and conservative, which can be a feasible tool for studying problems with moving boundaries.

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A consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain and transport of the body force; the pseudo body force defined at "solid centers" ensures the algorithm consists of the body force between the continuous form and its discretization counterpart; an explicit flux correction on cell faces and resulting mass source is introduced into the continuity equation to lower noncontinuity errors in the velocity correction step. This method is valid for stationary and moving boundary problems with arbitrarily polyhedral mesh.Several numerical tests are carried out to validate the proposed method. A second-order spatial accuracy is found in the flow around a cylinder case, and the spurious force oscillation is well suppressed for the in-line oscillation of a circular cylinder case. The performances on different meshes are tested, and structured mesh yields the best result, polyhedral next, and tetrahedral worst. A serial of tests is further performed on structured mesh to verify the effect of three different features (i.e., storing the body force at the solid centers, flux correction, and whether including the body force in the momentum equation) on the numerical predictions. Numerical results show that, in the in-line oscillation of a circular cylinder, "flux correction" can eliminate the large spikes in the drag coefficient, and "including the body force in the momentum equation" helps suppress the small oscillations. For other tests, "storing the body force at the solid centers" has enormous impacts on the final results of moving boundary problems, "flux correction" has little effects and the necessity of "including the body force in the momentum equation" is case dependent.