Lagrangian Radial Basis Function-Based Particle Hydrodynamics Method And Its Application For Viscous Flows

A Lagrangian radial basis function-based particle hydrodynamics method (RBFPH) is proposed. In RBFPH method, the differential quadrature technique is combined with radial basis function (RBF) to obtain the meshless high-dimensional derivative approximations for randomly distributed particles; a particular solution of RBF is chosen to ensure the positive definite of the interpolating matrix. Like the conventional RBF, RBFPH has the advantages of simple form, isotropy and high accuracy, and is suitable for numerical calculation. Moreover, all particles in RBFPH can move with the fluid, so RBFPH may conveniently compute complex flows with the moving boundary. A series of numerical examples are conducted to test the accuracy of RBFPH, and the results show the RBFPH has second-order convergence, which shows its great advantage in terms of accuracy. The RBFPH is validated by its application to the simulations of Taylor-Green flow, lid driven shear cavity flows, stretching of a free-surface circular fluid patch and flows around a cylinder. Excellent agreements with analytical solutions and reference results indicate that the proposed method has a promising application in simulating viscous flows with the moving boundary, large deformation, and free surface.