Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Comparison of Different Krylov Subspace Methods Embedded in an Implicit Finite Volume Scheme for the Computation of Viscous and Inviscid Flow Fields on Unstructured Grids

“…Furthermore, a large number of publications prove that these methods are widespread in numerical methods for real engineering applications [1,12,18,42,49,50,52,54,58,67,76,77]. However, a systematic investigation and comparison of Krylov subspace methods in combination with applicable preconditioning techniques is still missing.…”

A High-Resolution Procedure for Euler and Navier–Stokes Computations on Unstructured Grids

“…A higher order scheme not only yields improved resolution in regions of smooth flow but also significantly reduces the smearing of discontinuities. Initial attempts at implementation of higher order upwind schemes on unstructured grids focussed on extensions [4][5][6][7] of the one-dimensional reconstruction procedure based on the MUSCL approach [8], which had proved to be quite effective for structured-grid computations. However, because of the highly multidimensional nature of unstructured grids these techniques were only partially successful and it has been reported [9], but without numerical evidence, that poor quality results could be obtained on highly distorted grids even for smooth solutions.…”

Implicit Method for the Computation of Unsteady Flows on Unstructured Grids

“…It is the role of is usually unacceptably slow, especially as the problem these inner iterations to eliminate errors, if any, due to sizes and complexities grow. Therefore, either multigrid factorization and linearization, and sometimes also errors methods [21,30] or implicit schemes [37,44,2,4] are required to accelerate the convergence. On the other hand, arising from employing a lower order approximation on solution techniques for dealing with unsteady flows have the implicit side.…”