SPH Method Based Partly On Riemann Solution In Hydrodynamics And It’s Programing On GPU

The smoothed particle hydrodynamics(SPH) method is a meshless numerical methods, which is very important in the application of hydrodynamics. The CPU on the personal computer is not competent for the large-number no-logic computation duo to the larger number of particles when the SPH method is used to simulate the hydrodynamic problem, while compared with the computing speed of the CPU and the memory bandwidth of the CPU in the same periodic, when the graphic processing unit(GPU) is used for no-logic parallel computation, the computing speed of which is faster and the memory bandwidth of which is wider, so the advantages of the SPH method which is used for the simulation of the large deformation fluid and the GPU which is used for the parallel computation could be played out fully, while the general-purpose computing platform of GPU is applied to study the SPH method in the hydrodynamics.Although the SPH method is widely used in the hydrodynamics, there is the defect that the non-physical oscillations of pressure occurs when the traditional SPH method with the artificial viscosity term is used to simulate the static problem, the dam break problem, the solitary wave climbing problem and other hydrodynamic problem. To this end, the SPH method in the hydrodynamics was studied and the typical hydrodynamic problem with larger number of particles was simulated on the personal computer based on the GPU programing in this paper. The main contents in this paper are as follows:Firstly, the SPH method in the hydrodynamics was studied. In the simulation of the hydrodynamics, the non-physical oscillations of pressure, poor accuracy and stability occur by using the traditional SPH method with the artificial viscosity term and the pressure oscillation could be suppressed by using SPH method based entirely on the Riemann solution, but a larger numerical viscosity is introduced. In order to solve the problem, the weak compressible equation of state and the fluid control equations in the hydrodynamics were analyzed, and the SPH method based partly on the Riemann solution was proposed on this basis.Secondly, the modules of the SPH method based entirely on the HLLC first-order Riemann solution, the SPH method based partly on the HLLC first-order Riemann solution, the SPH method based entirely on the HLLC second-order Riemann solution and the SPH method based partly on the HLLC second-order Riemann solution, which were programed by the CUDA C, were added to the existing GPU program of the traditional SPH method with the artificial viscosity term, and then the GPU program containing a variety of modified SPH method in the hydrodynamics was obtained.Thirdly, a general-purpose computing platform of GPU was built on the personal computer, the code of the two-dimensional dam break problem model, the two- dimensional solitary wave climbing problem model, the three-dimensional static problem model, the three-dimensional dam break problem model and the three-dimensional solitary wave climbing problem model was programed, and by using the GPU program containing a variety of modified SPH method in the hydrodynamics, the two-dimensional dam break problem, the two-dimensional solitary wave climbing problem, the three-dimensional static problem, three-dimensional dam break problem and the three-dimensional solitary wave climbing problem were simulated on the general-purpose computing platform of GPU in this paper, and then the results of simulation were compared and analyzed.The results show that:(1)The SPH method based partly on the HLLC first-order Riemann solution and the SPH method based partly on the HLLC second-order Riemann solution could suppress the pressure oscillation effectively in the hydrodynamic problem, and the numerical viscosity of which is lower than the numerical viscosity of the SPH method based entirely on the HLLC first-order Riemann solution and the SPH method based entirely on the HLLC second-order Riemann solution, so the fluid motion characteristics of the typical hydrodynamic problem can be simulated realistically.(2)Based on the general-purpose computing platform of GPU and the programing, the hydrodynamic problem with the larger number of particles can be simulated on the personal computer by using the SPH method.