Finite element analysis of solitary wave propagation by acoustic velocity method

There is discontinuity between compressible and incompressible states in fluid flows. If we subtract the thermal effect from compressible fluid flows, we obtain adiabatic fluid flows, from which incompressible fluid flows are obtained if we let the acoustic velocity tend to infinity. Thus, we employ the idea of adiabatic fluid flows to solve incompressible flows. In the computation, the physical value of the acoustic velocity is employed. This idea corresponds to an extension of artificial compressibility under physical considerations. We present the new SUPG formulation of adiabatic fluid flows, by which not only the effect of SUPG but also those of PSPG and LSIC of incompressible fluid flows are derived. After the numerical verifications, three-dimensional solitary wave propagations are computed. Close agreement between computed and experimental values is obtained.