Performance of implicit methods in moving boundaryproblems

摘要

The Problem of relative motion of two parts of arnflying vehicle is of interest in a lot of practicalrnapplication. Numerical simulation of such problemsrnhas been developed during recent decades. Movingrngrid and numerical algorithm for solution of therngoverning equations are two main features of thernnumerical simulation. This paper deals with thernnumerical algorithms. The governing equations arerntime dependent and usually, solution of the equationsrnis performed using explicit methods. One of therndrawbacks of the explicit methods is that they arernlimited to small time steps due to the numericalrnstability problem. Such methods are not efficient forrnthe processes which their time scale is too small inrncomparison with the numerical time step size.rnSeparation of a booster from a spacecraft is anrnexample of such processes. For these processes,rnimplicit methods may have better performance. In thernpresent work, the performance of the implicitrnmethods is discussed for such processes. To do this,rnEuler equations are adopted as governing equationsrnand are solved in unstructured moving grids in tworndimensional spaces. The equations are solved usingrnfull implicit.rnFinally, for flow solution using full implicit methodrn(Generalized Minimal Residual (GMRES) methodrnwith preconditioner) leads to results with acceptablernaccuracy in a shorter time in comparison with explicitrnmethod.