Computational Fluid Dynamics (CFD-I)

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C- numerical solution(Leapfrog Scheme). The formula can be designed by approximating the space and time derivatives at by central differences.
Computational Fluid Dynamics -I (CFD-I) Session #8

STABILITY OF TRANSIENT SOLUTIONS (Part II)

Example #2 (fully implicit scheme for heat equation)

1. first-order forward difference in time 2. second-order central difference in space

3. Implicit

2

stability condition G(β)≤1is satisfied for any r ≥0

3

This conclusion is typical for implicit schemes. Many of them (but not all!) are unconditionally stable(i.e., stable for any choice of the time and space discretization steps)

A scheme is deemed stable if the entire curve G(β) at 0