Several Reseaches On Numerical Wave Simulation In The Interior Computational Domain

Numerical wave simulation is widely applied in large complexengineering problems. The aim for the technology of the numerical wavesimulation is to achieve high accuracy but low computation cost on conditionthat the simulation is steady. In this paper, high accuracy spectral elementmethod (SEM) and precise integration method (PIM) are studied. To deeplyunderstand the error and computation accuracy of simulation, it’s necessary torealize the property of wave propagation in the discrete grid. In this paper, theinfluence of wave propagation in the discrete grid by Rayleigh damp is alsodiscussed. The main contents are as follows:1. For SEM, the physical meaning of mass-lumping which depends onnumerical integration is given. The accuracy and steady condition of themethod for one dimension case are analyzed. The computation accuracy ofSEM and mass-lumping finite element method (FEM) is compared bynumerical test, based on the same computation cost.2. Combining PIM and FEM, a new method called PIM-FEM is deducedin one dimension. The accuracy and steady condition of this method areanalyzed. Comparing the dispersion curves of this method, central differenceFEM and semi-discrete ordinary differential equation attained by FEMdiscretization, it can be seen that the computation accuracy of semi-discreteordinary differential equation solved by PIM is higher than by centraldifference, but the computation accuracy of wave equation solved byPIM-FEM is lower than by central difference FEM. The accuracy matching ofthe space discrete method and the time discrete method is discussed, that isFEM with low accuracy is unsuited to combine PIM with high accuracy.These conclusions are verified by numerical test.3. Travelling wave analysis, vibration transfer analysis and Fourier modeanalysis are stated. The property of wave propagation in the discrete gird withRayleigh damp is studied by Fourier mode analysis. The forms of wavemotion in the discrete grid and cut-off wave number are presented and verifiedby numerical test. According to the dispersion and dissipation curves of thediscrete scheme deduced, the influence of wave propagation in the discretegrid by Rayleigh damp is discussed with specific parameters.