SIAM Journal on Scientific and Statistical Computing
Fronts, relaxation oscillations, and period doubling in solid fuel combustion
Journal of Computational Physics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Journal of Computational Physics
The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Numerical modeling of axisymmetric laminar diffusion flames
IMPACT of Computing in Science and Engineering
Towards polyalgorithmic linear system solvers for nonlinear elliptic problems
SIAM Journal on Scientific Computing
On performance of methods with third- and fifth-order compact upwind differencing
Journal of Computational Physics
A family of high order finite difference schemes with good spectral resolution
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion
Journal of Computational Physics
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
International Journal of High Performance Computing Applications
Hi-index | 31.45 |
A novel, stable, implicit compact scheme solver that is higher order in space, suitable for modeling steady-state and time-dependent phenomena on nonuniform grids for one-dimensional configurations, is presented. Several properties of compact scheme discretizations are introduced to develop efficient algorithms for Jacobian matrix generation and Jacobian-vector multiplication using a new component form for Jacobian operations. Composite nonuniform grids are introduced that enable the implicit compact scheme solver to achieve sixth order accuracy. A robust Newton's method is employed with explicit generation of Jacobian matrices. Superior resolution characteristics of the implicit compact scheme solver are demonstrated with several steady-state and time-dependent problems for the Burgers equation. The example of the solution of stiff flame problem is given. An analysis of spectral properties of Jacobian matrices is presented, which shows that the condition number and the eigenvalue distributions behave similarly to those found in Jacobians associated with low-order discretizations. Two sparsification strategies are developed for the systematic approximation of a dense Jacobian aimed at the practical implementation of linear system preconditioning through partial Jacobians.