Numerical simulation of free-surface flow and convection heat transfer using a modified Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method

Abstract

A novel Kernel Derivative-Free (KDF) Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) model is developed for simulation of free-surface flows and convection heat transfer. A high-order Laplacian operator is developed and then applied for the approximation of the diffusion terms (e.g., viscous term, thermal diffusion, and newly additional diffusion term in the continuity equation). The transient term in Navier–Stokes equation is discretized using the third-order TVD Runge-Kutta scheme, while a stiff equation of state is employed to predict pressure field. To increase numerical accuracy, a new high-order smoothing operator in the context of the MPS description (Moving Particle Semi-implicit) is also proposed and then applied for the treatment of the buoyancy force term in the momentum equation. Furthermore, a new high-order smoothing kernel is constructed and tested via simulation of the 1D Sod shock tube problem. A series of numerical benchmark cases such as: dam break, stretching of a circular water drop, rotating square patch of fluid and natural convection heat transfer in a square enclosure are used to verify and evaluate the feasibility of the proposed models. It is found that all simulation results are in excellent agreement with the available experimental and numerical data. Capability and performance of KDF-WCSPH method in handling particulate flows with thermal convection are further demonstrated through analysis of entropy generation due to natural convection heat transfer in the three different well-known geometries including: Differentially Heated Cavity, L-shaped enclosure and horizontal annuli. Comparison with the past Finite-Volume results demonstrates that the present model can maintain stability and accuracy, which makes it a very useful tool for simulation of thermo-hydraulic problems.