High Accuracy Numerical Computational Method For Euler/Navier-stokes Equations

By the use of polynomials reconstruction of flow values on the spatial stencil,and remaining the good property of high accuracy and high resolution,a new 5th order Finite Volume Weighted Essentially Non-Oscillatory(FVWENO5)scheme is constructed on the Cartesian grids.Together with the FVWENO5 scheme and the immersed boundary ghost cell methods(confining the boundary condition),the simulation of compressible flow problem around a complex body surface is fulfilled.Then,the FVWENO5 scheme combined with improved ghost cell method is applied in solving laminar Navier-Stokes equations.The main contents are as follows:(1)Constructing finite volume weighted essentially non-oscillatory scheme on the Cartesian gridsFirstly,an incompletely eighth degree polynomial is reconstructed on the big spatial stencil.Then the big spatial stencil is divided into nine smaller ones,and associated incomplete fourth degree polynomial is constructed on every smaller spatial stencil.After doing so,the linear weights,the smoothness indicators and the nonlinear weights for each stencil are computed.Together with the application of the third order TVD Runge-Kutta time discretization method,the fully high order accurate finite volume scheme both in space and time is obtained.(2)Confining the boundary condition with immersed boundary ghost cell methodsWhen performing simulations of complex body flow on Cartesian grids,a set of cutting cells are produced near the solid boundary,which leads to spurious oscillation of solution in the vicinity of the body and other problems.To make up the above disadvantages,three ghost cell methods are used to confine boundary condition.Several classical numerical tests containing the flow around a complex body are provided to verify the validity and accuracy of these methods.(3)Performing simulation of laminar flow on N-S equations with FVWENO5 schemeThe FVWENO5 scheme is expanded into the simulation of laminar flow,in which the inviscid flux terms are discretized with FVWENO5 scheme,and the second derivative viscous terms are approximated with central difference approximations.And then the improved ghost cell method is employed to confine non-slip boundary condition.Favorable computation results of laminar flow around a complex body prove the validity of the methods.