Limited to the calculation capability of computers and computational cost

some physical assumptions for flows are needed in the realistic simulation

such as inviscid flow

incompressible flow and so on

which will take various degrees of error in the simulation results. To solve this problem

a numerical method used to solve the weak compressible viscous flow is presented here that is capable to solve the weak compressible viscous flow whether there is a static or moving solid body in the flow field. Starting from the state equation of water

the velocity and pressure governing equations for weak compressible viscous flows are derived rigorously. Considering the effect of solid body

the Boundary Data Immersion Method (BDIM)

which can accurately represent moving bodies in flow and underwater acoustic simulations

is employed to couple the fluid sub-domain and solid sub-domain. Therefore

the flow field with the effects of the compression and viscosity is solved by coupling the weak compressible viscous flow and the BDIM. The effectiveness and accuracy of our method are validated by three two dimensional cases

and the results indicate that the novel method simulates the flow flied accurately and effectively for both a static and moving solid body.