Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations

摘要: Abstract Implicit methods for finite-volume schemes on unstructured grids typically rely a matrix-free implementation of GMRES and an explicit first-order accurate Jacobian preconditioning. Globalization is achieved using global timestep or CFL based local timestep. We show that robustness the globalization can be improved by supplementing pseudo-timestepping method commonly used with line search method. The number timesteps required convergence reduced scales residual. also it possible to form high-order explicitly at reasonable computational cost. This demonstrated cases both limited unlimited reconstruction. exact preconditioning directly in benefits improvements elimination residual evaluations inner iterations are substantial. Computational results focus second- fourth-order some third-order scheme. Overall cost matrix-explicit lower than all cases. scheme factor 1.6–3 faster while requiring about 50–100% more memory.