Combining Characteristic Forms of Boundary Conditions and Conversation Equations at Boundaries of Cell-Centered Euler-Flow Calculations

摘要

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. 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 asymptotically tend with time to prescribed steady-state values. The procedure for modeling such equations is explained with four examples. The procedure has been successfully tested numerically with 1D 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.