GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Spectral methods on triangles and other domains
Journal of Scientific Computing
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
An efficient implicit discontinuous spectral Galerkin method
Journal of Computational Physics
hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
SIAM Journal on Scientific Computing
Blending Finite-Difference and Vortex Methods for Incompressible Flow Computations
SIAM Journal on Scientific Computing
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Journal of Computational Physics
High-order discontinuous Galerkin methods using an hp-multigrid approach
Journal of Computational Physics
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
CFL Condition and Boundary Conditions for DGM Approximation of Convection-Diffusion
SIAM Journal on Numerical Analysis
Journal of Computational Physics
SIAM Journal on Scientific Computing
Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
Journal of Computational Physics
Efficient preconditioning for the discontinuous Galerkin finite element method by low-order elements
Applied Numerical Mathematics
On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
Journal of Computational Physics
Time Implicit High-Order Discontinuous Galerkin Method with Reduced Evaluation Cost
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
An efficient and robust time integration procedure for a high-order discontinuous Galerkin method is introduced for solving the unsteady compressible Navier-Stokes equations. The time discretization is based on an explicit formulation for the convective fluxes and an implicit formulation for the viscous fluxes. The implicit procedure uses a fast iterative algorithm based on a partial uncoupling of variables in neighboring elements introduced in previous works by the authors. In the present work, the method is associated to a Newton-Krylov Jacobian-free method. This association allows to reduce memory requirements and operation counts by avoiding the complete construction of the Jacobian matrix and solving a problem of reduced size. Numerical examples in two space dimensions indicate that the performance of the present method is seen to be significantly improved in terms of CPU time.