Combining characteristic forms of boundary conditions and conservation equations at boundaries of cell-centred Euler-flow calculations

Combining characteristic forms of boundary conditions and conservation equations at boundaries of cell-centred Euler-flow calculations

Boerstoel, J.W.

National Aerospace Laboratory NLR

1987-04-01

In Euler-flow calculations based on cell-centered schemes, the number of equations required to determine the flow-state evaluation at grid points half a mesh outside the flow domain usually exceeds the number of boundary-condition equations provided by characteristic theory. Here, the required additional equations are obtained by a physically well-defined numerical procedure, consisting of three steps. First, a layer of auxiliary cells on flow boundaries is introduced, and semi-discrete conservation equations for these cells are defined. Subsequently, the time variations of the state in these auxiliary cells at the boundary are transformed into characteristic form, and time variations of characteristic variables corresponding to incoming information from the boundary into the flow are replaced by boundary conditions for these time variations. In the third step, the boundary equations so obtained are mapped back into a form with primitive variables, and numerically integrated in time. The characteristic boundary conditions are first-order differential equations for time variations at boundary points of characteristic variables. These equations may be chosen to express that given functions of the flow state on the boundary should as3nnptotically tend with time to prescribed steady-state values. The procedure for modeling such equations is explained with four examples. The procedure has been succesfully tested numerically with ID Euler channel flows. The extension to 3D Euler flows is discussed. The characteristic boundary conditions are derived using a numerically and physically useful eigenvector-eigenvalue decomposition of the Jacobian matrices that appear in characteristic theory.

http://resolver.tudelft.nl/uuid:0a3893e2-5d80-49fa-95a3-297e21094387

Nationaal Lucht- en Ruimtevaartlaboratorium

Campus only

NLR MP 87024 U

Aerospace Engineering Reports

report

(c) 1987 National Aerospace Laboratory NLR