• Corpus ID: 246276110

A fully adaptive explicit stabilized integrator for advection-diffusion-reaction problems

@article{Almuslimani2022AFA,
  title={A fully adaptive explicit stabilized integrator for advection-diffusion-reaction problems},
  author={Ibrahim Almuslimani},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.10206}
}
We introduce a novel second order family of explicit stabilized Runge-Kutta-Chebyshev methods for advection-diffusion-reaction equations which outperforms existing schemes for relatively high Peclet number due to its favorable stability properties and explicitly available coefficients. The construction of the new schemes is based on stabilization using second kind Chebyshev polynomials first used in the construction of the stochastic integrator SK-ROCK. We propose an adaptive algorithm to… 

References

SHOWING 1-10 OF 23 REFERENCES
RKC time-stepping for advection-diffusion-reaction problems
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
TLDR
A new family of explicit integrators for stiff Ito stochastic differential equa- tions (SDEs) of weak order two is introduced, based on the standard second or- der orthogonal Runge-Kutta Chebyshev methods for deterministic problems.
An Implicit-Explicit Runge-Kutta-Chebyshev Scheme for Diffusion-Reaction Equations
TLDR
An implicit-explicit extension of the explicit Runge--Kutta--Chebyshev scheme designed for parabolic PDEs is proposed for diffusion-reaction problems with severely stiff reaction terms, which is unconditionally stable for reaction terms having a Jacobian matrix with a real spectrum.
Partitioned Runge-Kutta-Chebyshev Methods for Diffusion-Advection-Reaction Problems
  • C. Zbinden
  • Computer Science
    SIAM J. Sci. Comput.
  • 2011
TLDR
The aim of the PRKC method is to reduce the number of function evaluations of the nonstiff terms and to get a nonzero imaginary stability boundary.
On the Internal Stability of Explicit, m‐Stage Runge‐Kutta Methods for Large m‐Values
TLDR
It is shown that the value of m in the schemes proposed in this paper is not restricted by internal instabilities.
Explicit stabilized integrators for stiff optimal control problems
TLDR
This paper derives explicit stabilized integrators of orders one and two for the optimal control of stiff systems based on the continuous optimality conditions to analyze their favourable stability and symplecticity properties.
Second order Chebyshev methods based on orthogonal polynomials
TLDR
The aim of this paper is to show that with the use of orthogonal polynomials, the authors can construct nearly optimal stability polynmials of second order with a three-term recurrence relation.
Explicit Stabilized Methods for Stiff Stochastic Differential Equations and Stiff Optimal Control Problems
TLDR
New explicit stabilized methods for stiff and ergodic stochastic differential equations and for stiff optimal control problems are derived and analyzed rigorously their stability and convergence properties.
...
...