An Applied Study Of Preconditioning Method For Solving Euler Equations

In this paper two sets of computational codes are developed firstly for solving 2-D Euler equations by using finite-volume method on unstructured mesh and gridless algorithm on cloud of points , respectively. In the Euler solver developed, Jameson's finite-volume method and four-stage Rung-kutta time-stepping scheme are applied. Convergence is accelerated by means of local time-stepping and implicit residual smoothing. Then preconditioning methods for low-speed flow computations are investigated based on the codes developed. The basic concept of preconditioning method is described and two typical preconditioning methods are analyzed with preconditioning matrixes derived . Choi and Merkle's preconditioner and Pletcher and Chen's preconditioner are introduced successfully into the low-speed Euler solver. Numerical tests confirm that the Euler solver with present preconditioning does have fast convergence for low-speed flow simulations. Besides, a study of combining of gridless methods and preconditioning is also presented. Numerical results show that the gridless method with present preconditioner can solve the low-speed problems correctly.