Application of surface transpiration in computational aerodynamics

Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

“…In an integral formulation where W 1 , W 2 and * correspond respectively to two test functions and to a dimensionally consistent scalar product in R 4 , this can be written as follows: (30) defines v NS (c) as soon as c is given. The delicate point is that v NS (c) is defined on a domain X c which varies with c. The contribution of Hadamard and of other workers addressing this issue is to give a rigorous context to the differentiation of v NS (c) with respect to c. The reader interested in this theory can examine Refs.…”

Application of proper orthogonal decomposition to the discrete Euler equations

“…To avoid potential di culties associated with grid deformation and the ROM procedure described above, a transpiration boundary condition is applied at y = 0 to model the e ects of a moving boundary without grid deformation [23]. For the bump problem examined herein, the transpiration boundary condition involves the enforcement of the exact condition of impermeability at the panel surface,…”

An adaptive multitime multigrid algorithm for time-periodic flow simulations

“…This boundary condition is known as the transpiration boundary [18]. The geometry motion and grid motion need not coincide, and the difference is compensated by prescribing a transversal flow along the boundary (effectively a linearization of the correct boundary motion on the incorrect mesh).…”