Initial Boundary Value Problems

This chapter first discusses the initial boundary value problems in the advection and diffusion equations. The corresponding schemes to deal with the numerical boundary conditions such as extension scheme, unilateral difference scheme, similar Du Fort-Frankel scheme are introduced. In the second part, the boundary conditions in hydrodynamics problems are discussed, in which straight solid wall boundary condition, symmetric axis boundary condition, infinity boundary condition, and vorticity boundary condition are introduced to ensure the calculation stability and physical rationality. Finally, time-independent boundary value problem and the corresponding time-dependent methods are analyzed.