We report on a high-fidelity, spectral/hp element algorithm developed for the direct numerical simulation of thermal convection problems. consider incompressible Navier–Stokes (NS) and advection–diffusion equations coupled through body-forcing term. The flow is driven by prescribed flowrate forcing with explicit treatment nonlinear advection terms. body-force term also decouples both NS equatio...

In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is “exact” in that given the approximation inherent in the spectral-element method (SEM), no further approximation is introduced that exceeds computer round-off error. The method is very useful when the SEM has yielded an ada...

Article history: Received 25 April 2008 Received in revised form 13 August 2008 Accepted 14 August 2008 Available online 29 August 2008

The Method of Transformed Field Expansions (TFE) has been demonstrated to be a robust and highly accurate numerical scheme for simulating solutions of boundary value and free boundary problems from the sciences and engineering. As a Boundary Perturbation Method it builds highly accurate solutions based upon exact solutions in a simple, canonical, geometry and corrects these via Taylor series to...