Numerical modelling of some two-phase fluid flow problems Original Research Article

Hydrodynamic (fluid flow) problems in general are actual from the wide points of view. The ecological catastrophe in the Czech Republic (2002), especially flooding of Pilsen, gives us new impulses for numerical simulation of particular fluid flow problems. Here we discuss two variants of mathematical fluid flow models: the multiphase compressible inviscid fluid flow model and the multi-component incompressible viscous fluid flow model. The first type of fluid flow problems is oriented to modelling the steam flow with the population of the condensation nuclei of chemical impurities in power equipment. In this case, our global mathematical model (with turbulent structure) has the form ∂U∂t+∂F(U)∂x+∂G(U)∂y=H(U), i.e., consists of PDE system of 10 equations. Here, we connect the macroprocess of the steam flow described by standard conservation laws with microprocesses of evolution of condensation nuclei. The last six equations of our system are taken in the form of the transport law ∂ρQi∂t+div(ρQiv)=h(U) where ρQi are some components of the vector U (describing the sort of the condensation particles, their quantity, volume, etc.). In our simulations, we compare the higher-order relaxation schemes and the monotonic upstream schemes (MUSCL) based on the Godunov approach. In the second model, we consider the problem with the moving interface of different components of the fluid. The movement of the interface will be described by a special transport equation (volume fraction equation) with zero inlet boundary condition. This model gives a possibility to simulate the oil–water flow after oil spill as a flow of two immiscible incompressible viscous components.