A robust weakly compressible SPH method and its comparison with an incompressible SPH

Abstract

This paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering-induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods.transfer problems [11], among others. In this method, rather than using an Eulerian fixed mesh, the computational domain is represented by a set of particles that are allowed to move in accordance with the solutions of relevant governing and constitutive equations. In fact, here, the term particle merely refers to a movable point that is bestowed with relevant physical and hydrodynamic transport properties such as temperature, density, viscosity and so forth. The Lagrangian nature of SPH lends itself remarkably to the simulation of a variety of complex fluid flow processes such as flow around bluff-bodies.In the SPH literature, there are two commonly utilized approaches for solving the balance of the linear momentum equations; namely the Incompressible SPH (ISPH), and the Weakly Compressible SPH (WCSPH) methods.The ISPH technique is based on the projection method originally proposed in [12,13] and first implemented to the SPH method in the work of Cummins and Rudman [14], which is referred to as the standard projection method in this work. In this method, the pressure term in the momentum balance equation is computed by solving a pressure Poisson's equation. The standard projection method has been reported to suffer from the density error accumulation during the computation of the intermediate density field [15,16]. To circumvent this and the associated problems, and consequently enhance the accuracy and the performance of the standard ISPH scheme, several modifications have been proposed for it in literature. For example, Shao and Lo [15] enforced the incompressibility in a somewhat similar manner to the one proposed in [14] with two main differences: first, they computed the intermediate velocity and then advected SPH particles; and second, they utilized the density variation as a source term rather than the divergence of the intermediate velocity. Their projection scheme has been re...

Modified MPS method for the 2D fluid structure interaction problem with free surface

“…As a consequence, the DF approach is reported to suffer from the particle clustering and void, which will result in density error accumulation and bad pressure distribution [17,18]. On the other hand, the DI type source will lead to large density variation (probably caused by the full inclusion of accumulated density error), and consequently large pressure fluctuations in both spatial and temporal domain [19]; which reduce the stability of the pressure computation.…”

“…Many researchers have developed some techniques to handle this problem [13,14,16,17,27,28]. Among these improvements, rearranging the particle…”

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