An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids

An accurate, fast, matrix-free implicit method has been developed to solve the three-dimensional compressible unsteady flows on unstructured grids. A nonlinear system of equations as a result of a fully implicit temporal disc retization is solved at each time step using a pseudo-time marching approac h. A newly developed fast, matrix-free implicit method is then used to obta in the steady-state solution to the pseudo-time system. The developed metho d is applied to compute a variety of unsteady how problems involving moving boundaries. The numerical results obtained indicate that the use of the pr esent implicit method leads to a significant increase in performance over i ts explicit counterpart, while maintaining a similar memory requirement. (C ) 2000 Elsevier Science Ltd. All rights reserved.