Spectrally accurate algorithm for analysis of convection in corrugated conduits

An algorithm suitable for analysis of convection problems in corrugated conduits has been developed. The algorithm uses the immersed boundary conditions (IBC) concept to capture the effects of corrugated walls. The field equations are discretized on a regular domain surrounding the flow domain using Fourier expansions in the stream-wise direction and Chebyshev expansions in the wall-normal direction. The boundary conditions are expressed in the form of constraints and the spectrally accurate discretization of these constraints is discussed. The solution is carried out using the fix flow rate constraint. Discretization as well as a method for the direct inclusion of this constraint in the flow solver is presented. Several tests are used to demonstrate the spectral accuracy of the solution. The solution process relies on iterations with an efficient solver taking advantage of the structure of the coefficient matrix used to solve the linear system. The limitations of the algorithm are discussed and gains associated with the over-determined formulation are presented.