Conservation Equations in General Curvilinear Coordinate Systems
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In 1974 Vivand and Vinokur published their remarkable works on conservation equations of gas dynamics in curvilinear coordinate systems. Since that time there have been many publications on different aspects of this topic. Several providers of computational fluid dynamics tools use the developed strategy for single-phase flows in attempting to extend the algorithm for multi-phase flows. The usually used approach is to write all partial differential equation in convection-diffusion form and to use the already existing transformations and numerical algorithms for single-phase flow. What remains outside the convection-diffusion terms is pooled as a source into the right hand side. The problems with this approach are two: (a) the remaining terms can contain substantial physics represented in differential terms and (b) the realized coupling between the equations is weak. The latter is manifested if one tries to use such codes for processes with strong feedback of the interfacial heat and mass transfer processes on the pressure, e.g. steam explosion, spontaneous flashing etc.
KeywordsConservation Equation Versus Versus Versus Steam Explosion Mass Conservation Equation Curvilinear Coordinate System
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