A meshless solution of a of lid-driven cavity containing a heterogeneous porous medium

The main objective of the present paper is to define and evaluate a benchmark test for solving the Navier-Stokes equations in heterogeneous porous medium. The benchmark is of high relevance for proper numerical simulation of flow pattern in the liquid-solid phase-change related phenomena. The test case represents a lid-driven square cavity which consists of a solid, a liquid, and a mushy part. Three different variations of the problem are solved, in which the ratio between the liquid and the mushy part is modified. The Reynolds and the Darcy number of this case are equal to 400 and 2.5×10−10, respectively. The Navier-Stokes equation, with an additional source term to take into account the Darcy effect, is solved with the local meshless diffuse approximate method. The method is structured by using the second-order polynomial basis vector and the Gaussian function to evaluate the weighted least squares approximation. The explicit Euler scheme is used to perform the time discretisation. The non-incremental pressure correction scheme is used to couple the pressure and velocity fields. Results are presented in terms of stream function, velocity magnitude, and mid-plane velocity profiles in the steady state. The accuracy of the numerical method is evaluated by a comparison with the finite volume solution obtained with a commercial solver and an investigation of the node arrangement effect.