Integration factor combined with level set method for reaction-diffusion systems with free boundary in high spatial dimensions

@article{Liu2022IntegrationFC,
  title={Integration factor combined with level set method for reaction-diffusion systems with free boundary in high spatial dimensions},
  author={Shuang Liu and Xinfeng Liu},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.15095}
}
For reaction-diffusion equations in irregular domain with moving boundaries, the numerical stability constraints from the reaction and diffusion terms often require very restricted time step size, while complex geometries may lead to difficulties in accuracy when discretizing the high-order derivatives on grid points near the boundary. It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties. Applying an implicit scheme may be able to remove the… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 60 REFERENCES

Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness

A universally applicable embedded boundary embedded boundary method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness, is developed.

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

A numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions using a finite-volume discretization, which embeds the domain in a regular Cartesian grid.

A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains

Interfaces have a variety of boundary conditions (or jump conditions) that need to be enforced. The Ghost Fluid Method (GFM) was developed to capture the boundary conditions at a contact

Numerical Methods for a Class of Reaction-Diffusion Equations With Free Boundaries

The spreading behavior of new or invasive species is a central topic in ecology. The modelings of free boundary problems are widely studied to better understand the nature of spreading behavior of

A Second Order Accurate Embedded Boundary Method for the Wave Equation with Dirichlet Data

A numerical method is developed where both the solution and its gradient are second order accurate and long-time stability of the method is obtained by adding a small fourth order dissipative term.

Fourth-Order Time-Stepping for Stiff PDEs

A modification of the exponential time-differencing fourth-order Runge--Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as

A comparison of implicit time integration methods for nonlinear relaxation and diffusion

Removing the stiffness from interfacial flows with surface tension

A new formulation and new methods are presented for computing the motion of fluid interfaces with surface tension in two-dimensional, irrotational, and incompressible fluids. Through the
...