Study and application of pollutant diffusion based on SPH method

In this paper, the meshless smooth particle hydrodynamics (SPH) method is used to simulate the transport process of pollutants in the environment by solving the convection-diffusion equation of pollutants under the Lagrangian framework. This method avoids various numerical problems caused by mesh distortion or mesh movement and the calculation of the derivative of the kernel function when approximating the second derivative kernel. In order to reduce the original virtual particle method of SPH to solve the boundary problem due to the large amount of particle searches will increase the amount of redundant calculation and other factors, selected with the finite difference method to solve the boundary. To verify the proposed Lagrangian particle model, numerical experiments were carried out. The one-dimensional calculation results are compared in detail with the results of different schemes in the finite difference method, and the L2, L & INFIN; and relative errors are analyzed. The simulation results show that the SPH-based model requires fewer particles. In addition, the model is numerically analyzed under the condition of ensuring accuracy. The numerical solution is in good agreement with the analytical solution. The research results of this paper can provide a new solution and idea for environmental pollution early warning.