Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
On error growth functions of Runge-Kutta methods
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
Microstructural evolution in orthotropic elastic media
Journal of Computational Physics
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Efficient semi-implicit schemes for stiff systems
Journal of Computational Physics
Compact integration factor methods in high spatial dimensions
Journal of Computational Physics
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Compact integration factor methods for complex domains and adaptive mesh refinement
Journal of Computational Physics
Numerical Methods for Two-Dimensional Stem Cell Tissue Growth
Journal of Scientific Computing
Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations
Journal of Computational Physics
Array-representation integration factor method for high-dimensional systems
Journal of Computational Physics
Hi-index | 31.46 |
For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction-diffusion systems with both stiff reaction and diffusion terms, implicit integration factor (IIF) method and its higher dimensional analog compact IIF (cIIF) serve as an efficient class of time-stepping methods, and their second order version is linearly unconditionally stable. For nonlinear hyperbolic equations, weighted essentially non-oscillatory (WENO) methods are a class of schemes with a uniformly high order of accuracy in smooth regions of the solution, which can also resolve the sharp gradient in an accurate and essentially non-oscillatory fashion. In this paper, we couple IIF/cIIF with WENO methods using the operator splitting approach to solve reaction-diffusion-advection equations. In particular, we apply the IIF/cIIF method to the stiff reaction and diffusion terms and the WENO method to the advection term in two different splitting sequences. Calculation of local truncation error and direct numerical simulations for both splitting approaches show the second order accuracy of the splitting method, and linear stability analysis and direct comparison with other approaches reveals excellent efficiency and stability properties. Applications of the splitting approach to two biological systems demonstrate that the overall method is accurate and efficient, and the splitting sequence consisting of two reaction-diffusion steps is more desirable than the one consisting of two advection steps, because CWC exhibits better accuracy and stability.