Numerical Simulation Of Shock Interacting With Interfaces

A moving shock interacted with multi-material interfaces are studied in this thesis.The gas and water are assumed as inviscid and compressible fluid and flow-field is described by Euler equations.GFM method is extended for boundary treatment at multi-material interfaces and computational domain.Moving interfaces are captured by level-set method.In processing the interface boundary conditions,some properties of ghost and local real fluids are considered simultaneously.The boundary conditions at gas-gas interface are defined by OGFM method.A refined rGFM method which improves the construction of Riemann problem is used to define the boundary conditions at gas-water interface.Referring to the GFM method,extrapolation is applied for the gas-solid interface boundary conditions.Euler equations in hyperbolic formulism,level-set equation and re-initialization equations in Hamilton-Jacobi formulism are solved by finite difference methodology.Specialized 5th order WENO schemes and 3rd order TVD Runge-Kutta method are respectively applied for spatial and time discretization.Numerical examples in references are firstly repeated for code validation.Such as Sod and Lax shock tube problems,interface motions in rotating and shearing flows,un-derwater gas bubble expansion and shock interacting with single water or solid cylinder.Results are in good accordance with those in the references.Then the computations are carried out on a shock interacting with double rows of water or solid columns,single row of water columns and multi-interfaces including a Helium bubble,a water column and a solid cylinder.Numerical schlieren images at different instants and pressure time histories at specified points are provided.Conclusions are summarized as follows:(1)For shock interacting with double rows of water or solid columns,the results show that shock regular and Mach reflections occur at interfaces.The transmitted shock is very weak inside the water due to less absorption of energy from the air inci-dent shock.Furthermore,shock reflection and Mach reflection happen either on the neighbouring interfaces of the rows which originates from the previous shock propagation and generate very complex shock structures.Almost identical shock structures are derived for geometry with the same size of water and solid except no transmitted shock wave inside the solid.Due to high density and inertia of water,the water column hardly moves during shock passing through it.Energy absorbed by water is very small because of large difference of acoustic impedance between water and air.Vortexes appear downstream of water and solid cylinders.(2)For shock interacting with different diameters and numbers of water columns in a single row,the results indicate that the more water columns leads to less void fractions in the geometry and the shock is disturbed more seriously.The curved shocks appear downstream the throat between neighbouring cylinders of water and solid which is quite similar to a starting shock in vicinity of a nozzle exit.(3)For shock interacting with a helium bubble,a water column and a solid cylinder simultaneously,the results show that different shock structures appear on gas,wa-ter and solid interfaces.Shock structures and strength on water and solid interfaces are almost identical.However,on the helium interface,the shock structures change violently and the transmitted shocks inside the helium bubble attenuate very much because of the same extent of acoustic impedance between helium and air.In con-trast to water,the transmitted shock in helium bubble is much stronger since more energy is absorbed from the air shock.(4)Again,the results demonstrate that numerical methods and treatments of the in-terface boundary conditions in this thesis are capable of capturing the complex shock structures which generated from a shock interacting with multi-interfaces.The GFM method used in gas-gas and gas-water interfaces boundary description is extended to the cases of gas-solid interfaces and computational domain.Different from coordinate transformation,this provide a new way for dealing with complex geometry computation even with moving boundaries.