.euler / Ns Equation Modeling With Multi-grid Method

Computational fluid dynamics methods are now routinely applied to study many complex flow phenomena that are difficult or even impossible to study experimentally. With the rapid advances in computer hardware and computation technology, solution of the full Navier-Stokes equation, or the Reynold-averaged form, have been found to yield realistic simulations of the flow characteristics. However, even for the Reynold-averaged form approximation, the computational cost is often too expensive where quantitative accuracy is required. To reduce cost, acceleration techniques such as residual smoothing, local time stepping, enthalpy damping, and multigrid are introduced. Thus far, multigrid is considered the most effective. Structurally, multigrid algorithms iterate on a hierarchy of successively coarser grids to acceleration convergence on the finest grid.According to the aspect, the major works of this paper are as follows: 1. Using elliptic grid generation method with orthogonality and spacing control generate two dimension inviscous grids, and together with an algebraic method marching along the normal-to-wall direction generate two dimension viscous grids.2. The 2D Euler code based on Jameson's central finite volume method was compiled, and at the same time, the code was upgraded to N-S program though modified artificial viscosity and added the B-L turbulent model. Complex boundary conditions were simplified by adopting "ghost" cell, and in order to improve the computational efficiency, local time step, variable coefficients implicit residual smooth and enthalpy damping were used. Finally, the 2D Euler and N-S code was extend to 3D.3. Convergence acceleration techniques based on the multigrid methods were developed for solving 2d and 3d compressible Euler and N-S equations. In order to solve the grid-induced slow convergence (because the large aspect ratios) in solving N-S equations, semi coarsening multigrid method was used in 2d N-S code.4. NACA0012, NACA4412, RAE2822 airfoil and ONERA M6 wing, delta wing, slender body of missile and TND-712 wing-body standard model were chosen to confirm the validity of the current multigrid method. The numerical examples show that the current multigrid method is efficient and robust forsolving of both 2D and 3D Euler and N-S equations.