"There is a subtle difference between the integral and differential forms of the governing flow equations which is best noted at this stage. The integral form of the equations allows for the presence of discontinuities inside the fixed control volume(fixed in space); there is no mathematical reason t"
"This motivation is driven by more than just trying to minimize the truncation error with closely spaced points; it is also a matter of simply having enough grid points to properly capture the physics of the flow(in those regions of the flow where large gradients in the flow-field properties exist)."
"The numerical solution of a partial differential equation is influenced by two sources of errors: Discretization error, the difference between the exact analytical solution of the partial differential equation and the exact solution of the corresponding difference equation. From the discussion in Se"
"In pricinple, we can only hope that the numerical results give values for T which represent those that would be obtained from a closed-form analytical solution of the original partial differential equation, at least within the truncation error. Some confidence in this regard can be ontained if we ca"
"If the round-off error are already present at some stage of the solution of the equation(as they always are in any real computer solution), then the solution will be stableif the round-off error shrink, or at best stay the same, as the solution progresses from step n to n+1."
"Because the conservation form of the equations does a better job of conserving mass throughout the flow field, we can begin to understand why they are labeled the conservation form."