Discretization methods (Cont’d)
Explicit methods can be easily applied but yield conditionally stable Finite Different Equations (FDEs), which are restricted by the time step; Implicit methods are unconditionally stable, but need efforts on efficiency.
Usually, higher-order temporal discretization is used when the spatial discretization is also of higher order.
Stability: A discretization method is said to be stable if it does not magnify the errors that appear in the course of numerical solution process.
Pre-conditioning method is used when the matrix of the linear algebraic system is ill-posed, such as multi-phase flows, flows with a broad range of Mach numbers, etc.
Selection of discretization methods should consider efficiency, accuracy and special requirements, such as shock wave tracking.