A streamline derivative POD-ROM for advection-diffusion-reaction equations

Numerical Solution of Advection-Diffusion-Reaction Equations

Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

The LEM exponential integrator for advection-diffusion-reaction equations ⋆

We implement a second-order exponential integrator for semidiscretized advectiondiffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by Finite Differences or Finite Elements, show that the Leja-Euler-Midpoint ...

Streamline Design of Stability Parameters For Advection-diffusion Problems

The dependence of the computation of advective-diffusive transport phenomena on the orientation of the mesh with respect to the flow direction is analyzed. Poor performance of the classical Galerkin finite element method in the convectiondominated regime is alleviated by stabilization. We propose definitions of the stability parameter that rationally incorporate the flow direction. Numerical te...

positivity-preserving nonstandard finite difference schemes for simulation of advection-diffusion reaction equations

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...