A numerical method for solving atmospheric condensate flows at very low Mach number is proposed. This method is based on the preconditioning method proposed by Weiss and Smith, the fourth-order compact MUSCL scheme, the Roe's approximate Riemann Solver, and the LU-SGS scheme. The fundamental equations for atmospheric condensate flows have been developed by the authors. The continuity equation of mixed gas, the momentum equations, the energy equations, the continuity equation of vapor, the continuity equation of liquid, and the continuity equation of the number density of atmospheric small particles are solved by the present preconditioned implicit method simultaneously. The fundamental equations are transformed to the preconditioned equations. The preconditioned Roe's scheme and the preconditioned LU-SGS scheme(1) are newly derived by introducing a preconditioned implicit flux-splitting form(2) which can be applied not only to the explicit calculation but also to the implicit calculation.

Calculate results 1，２，３，４，５，６，７，８，９，１０

References

Satoru Yamamoto and Byong-Rog Shin, Preconditioned Implicit Flux-splitting Scheme for Condensate Flows, Proc. 2nd ICCFD, Computational Fluid Dynamics 2002, 2002, 112-117, Springer.

Satoru YAMAMOTO, Byeong-Rog SHIN and Daisuke NIIYAMA, Preconditioning Method for Heterogeneous Condensate Flows, Proceedings of the Fifth JSME-KSME Fluids Engineering Conference, (2002), CD-ROM.

Satoru YAMAMOTO and Daisuke NIIYAMA, Byeong Rog SHIN, PRECONDITIONED HIGH-RESOLUTION SCHEME FOR GRAVITATIONAL FLOWS WITH CONDENSATION, Proceedings of FEDSM’03, 4th ASME_JSME Joint Fluids Engineering Conference, FEDSM2003-45390, (2003), CD-ROM.

Kei Sakakura, Satoru Yamamoto and Yasuhiro Sasao, Preconditioning Method for Very Slow Flows with Heterogeneous Condensation in Mixing T Junction Channel, Proceedings of ASME Fluids Engineering Summer Conference, FEDSM2005-77073(2005), CD-ROM.

Kei Sakakura and Satoru Yamamoto, Numerical and Experimental Predictions of Heterogeneous Condensate Flow of Moist Air in Cooled Pipe, International Journal of Heat and Fluid Flow, (2005), accepted for publication.