Exact non-reflecting boundary conditions
Journal of Computational Physics
Fast adaptive methods for the free-space heat equation
SIAM Journal on Scientific Computing
Journal of Computational Physics
On nonreflecting boundary conditions
Journal of Computational Physics
High-Order Radiation Boundary Conditions for the Convective Wave Equation in Exterior Domains
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Computational Solution of Blow-Up Problems for Semilinear Parabolic PDEs on Unbounded Domains
SIAM Journal on Scientific Computing
Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in R2
Journal of Scientific Computing
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The numerical solution of the two-dimensional Burgers equation in unbounded domains is considered. By introducing a circular artificial boundary, we consider the initial-boundary problem on the disc enclosed by the artificial boundary. Based on the Cole-Hopf transformation and Fourier series expansion, we obtain the exact boundary condition and a series of approximating boundary conditions on the artificial boundary. Then the original problem is reduced to an equivalent problem on the bounded domain. Furthermore, the stability of the reduced problem is obtained. Finally, the finite difference method is applied to the reduced problem, and some numerical examples are given to demonstrate the feasibility and effectiveness of the approach.