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In this paper, we propose two numerical methods for a fluid mixture model. The model is usually used to describe the tissue deformations. It contains a nonlinear hyperbolic equation and an elliptic equation. The first numerical method is the generalized difference method based on linear element function space and piecewise constant function space. Numerical experiments show that our scheme is second-order accuracy in space. To eliminate the oscillation near the discontinuities, we design a generalized upwind difference method to solve the fluid model. Numerical results show that the two methods are effective for the considered fluid mixture model.
Wave-generating technology is becoming more and more mature with the development of the computer technology. Compared with physical experiment, it is easier for implementation and lower at cost. The numerical wave tanks are the frontiers of the shipbuilding and ocean engineering hydrodynamic fields in these days. Velocity-inlet boundary wave generating and mass source wave generating are the common methods. In this paper, both of the two methods are used for the simulation of numerical wave tank and the results are satisfactory. High precision and low attenuation are the merits of mass source wave generating, while velocity-inlet boundary wave generating has the advantage of easy implementation and good algorithm convergence. In general, mass source wave generating is better. Research in this paper can serve as a foundation for the simulation of numerical waves in structure-wave problems.