NUMERICAL-SIMULATION OF VISCOUS-FLOW BY SMOOTHED PARTICLE HYDRODYNAMICS

Smoothed particle hydrodynamics (SPH) is an effective numerical method to solve various problems, especially in astrophysics, but its applic ations have been limited to inviscid flows since it is considered not to yield ready solutions to fluid equations with second-order derivati ves. Here we present a new SPH method that can be used to solve the Na vier-Stokes equations for constant viscosity. The method is applied to two-dimensional Poiseuille flow, three-dimensional Hagen Poiseuille f low and two-dimensional isothermal flows around a cylinder. In the for mer two cases, the temperature of fluid is assumed to be linearly depe ndent on a coordinate variable x along the flow direction. The numeric al results agree well with analytic solutions, and we obtain nearly un iform density distributions and the expected parabolic and paraboloid velocity profiles. The density and velocity field in the latter case a re compared with the results obtained using a finite difference method . Both methods give similar results for Reynolds number R(e)=6, 10, 20 , 30 and 55, and the differences in the total drag coefficients are ab out 2 similar to 4%. Our numerical simulations indicate that SPH is al so an effective numerical method for calculation of viscous flows.