A simple Eulerian-Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

In this article, we propose a simple, consistent, and robust Eulerian-Lagrangian weakly compressible smoothed particle hydrodynamics (EL-WCSPH) for the simulation of hydrodynamics and convection heat transfer problems. First, the basic governing equation is formulated using the ALE-SPH framework. The universal formulation is similar to the standard WCSPH, but the degree of Eulerian and Lagrangian schemes can be controlled by inserting a pre-defined arbitrary parameter alpha is an element of[0,1]$$ \upalpha \in \left[0,1\right] $$. To alleviate potential numerical errors and inconsistency, particle mass correction is proposed along with particle disorder correction. Then, an algorithm is introduced, in which only a slight modification is necessary compared to the standard WCSPH. Finally, extensive benchmark simulations are conducted to validate the proposed method. As a result, the proposed method is found to perform well in hydrodynamics problems with various flow conditions (pipe flow, lid-driven problem, Taylor-Green vortex, vortex shedding problem, and water sloshing) and thermal-hydraulics problems (natural convection in a square cavity).

Automated summary

In this article, a simple, consistent, and robust Eulerian-Lagrangian weakly compressible smoothed particle hydrodynamics (EL-WCSPH) method is proposed for simulating hydrodynamics and convection heat transfer problems. The method utilizes the ALE-SPH framework and allows control of the degree of Eulerian and Lagrangian schemes using a predefined parameter alpha. To address potential numerical errors and inconsistency, particle mass correction and particle disorder correction are introduced. Extensive benchmark simulations confirm the effectiveness of the proposed method in various hydrodynamics and thermal-hydraulics problems.