On Operator Splitting for Unsteady Boundary Value Problems.
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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A frozen Jacobian locally linearized analysis and again matrix approach is used to argue that a certain operator splitting of the two-dimensional, conservation form, Navier-Stokes equations is second-order accurate. MacCormacks intuitive result, which through the above approach can rigorously be shown valid only for linear systems, is also true in the presence of nonlinearity. Additional second-order splittings are obtained for the case in which derivative-free source terms are present in the fluid dynamics equations. Some discussion of operator optimality is given.
- Fluid Mechanics