Mixture-Slip Flux Splitting for Numerical Computation of 1-DTwo-Phase Flow
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In this thesis we are dealing with the numerical computation of the one dimensionaltwo-fluid model. The main objective has been to develop a robust numericalmethod for incompressible flow which can be applied for both gas-liquidflow and liquid-liquid flow. A new finite volume method called the Mixture-SlipFlux Splitting (MSFS) method is proposed. This method distributes the numericalmass and momentum fluxes onto a mixture flux and a slip flux, using thesign of the mixture velocity and the slip velocity to determine the upstream values.This method has demonstrated good stability properties for the challengingproblem with transition to single phase flow, but is in general less accurate thanthe traditional upstream methods. In order to solve the incompressible two-fluid model with good accuracy inthe two-phase domain, we proposed a Roe scheme with a novel Roe matrix forthe incompressible two-fluid model. The Roe scheme was also extended to 2ndorder. The Roe scheme and the MSFS method was then combined into a hybridmethod where the Roe scheme was used in the two-phase flow area and theMSFS method was used in the single phase area. This hybrid method allowedfor good accuracy in two phase flow while it made it possible to simulate intothe single phase flow area. The hybrid Roe-MSFS method was then used to simulate slug flow usingthe slug-capturing technique. In order to remedy the ill-posedness of the twofluidmodel, a mathematical motivated term was added to the equation setwhich made the two-fluid model unconditionally hyperbolic. The result fromthe slug-capturing simulations showed that the results were sensitive to boththe time step and the grid resolution. Moreover, as the grid was refined the slugdistribution did not converge to a unique solution. The MSFS method was also tested for compressible two phase flow. For thispurpose we used a staggered grid and applied the MSFS discretization methodfor the mass fluxes. In this case we observed improved numerical behavior forthe single phase transition compared to a classical upstream method. However,in the two phase region for purely upstream conditions the MSFS method failedto converge.