A method to trace sharp interface of two fluids in calculations involving shocks. (English) Zbl 0820.76063
The paper concerns with tracing contact discontinuities described by the fluid dynamics equations written in the Eulerian form. Upon splitting the flow equations into the advection and acoustic parts, the advection equation for the transformed density function is introduced. It is stated that the solutions of the resulting set of equations can provide contact discontinuities as sharp fronts described by two grid points. Examples are presented for both compressible and quasi-incompressible flows.
Reviewer: A.I.Tolstykh (Moskva)
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
Keywords:
contact discontinuities; advection equation; transformed density functions; quasi-incompressible flowsReferences:
| [1] | Daly BJ (1969) A technique for including surface tension effects in hydrodynamic calculations. J Comput Phys 4:97 · Zbl 0197.25301 · doi:10.1016/0021-9991(69)90042-4 |
| [2] | Harlow FH, Amsden AA (1968) Numerical calculation of almost incompressible flow. J Comput Phys 3:80 · Zbl 0172.52903 · doi:10.1016/0021-9991(68)90007-7 |
| [3] | Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundary. J Comput Phys 39:201 · Zbl 0462.76020 · doi:10.1016/0021-9991(81)90145-5 |
| [4] | Nichols BD, Hirt CW (1971) Improved free surface boundary conditions for numerical incompressible-flow calculations. J Comput Phys 8:434 · Zbl 0227.76048 · doi:10.1016/0021-9991(71)90022-2 |
| [5] | Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100:25 · Zbl 0758.76047 · doi:10.1016/0021-9991(92)90307-K |
| [6] | Wang PY, Yabe T, Aoki T (1993) A general hyperbolic solver ? the CIP method applied to curvilinear coordinate. J Phys Soc Japan 62:1865 · Zbl 0972.65510 · doi:10.1143/JPSJ.62.1865 |
| [7] | Yabe T, Ishikawa T, Wang PY, Aoki T, Kadota Y, Ikeda F (1991) A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers. Comput Phys Comm 66:233 · Zbl 0991.65522 · doi:10.1016/0010-4655(91)90072-S |
| [8] | Yabe T, Wang PY (1991) Unified numerical procedure for compressible and incompressible fluid. J Phys Soc Japan 60:2105 · doi:10.1143/JPSJ.60.2105 |
| [9] | Yabe T, Mochizuki T, Hara H (1992) Multi-dimensional hydrodynamic simulation of laser-induced evaporation dynamics. In: Matsunawa A, Katayama S (eds) Proc of laser advanced materials processing (LAMP) ’92, Nagaoka, Japan, June, 1992. pp 387-392 |
| [10] | Yabe T, Xiao F (1993) Description of complex and sharp interface during shock wave interaction with liquid drop. J Phys Soc Japan 62:2537 · doi:10.1143/JPSJ.62.2537 |
| [11] | Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31:335 · Zbl 0416.76002 · doi:10.1016/0021-9991(79)90051-2 |
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