低マッハ数近似に対する陽的ルンゲクッタ・射影法の適用

抄録

When applying explicit Runge-Kutta methods to the system of equations derived from low-Mach number approximation, order reduction of the dynamic pressure may occur. It is discussed in the present account that the reduction of temporal order occurs because time derivative of the density or the dynamic pressure (or the Bernoulli function) is included in the source term of the Poisson equation, or in the computation of divergence of the velocity, respectively, depending on the algorithms. The situation is analogues to the case of the governing equations for the incompressible fluid flows. For the incompressible flows, temporal derivative of the velocity at the boundaries is approximated by a finite difference formula, whose coefficients are computed from the coefficients of the Runge-Kutta method, used for the temporal integration of the velocity. The order of accuracy of the finite difference formula is not same as that of the Runge-Kutta method, except for particular cases. In the present account, the remedy to recover the order of accuracy of the pressure is proposed for the system of low-Mach number approximation equations.