Global coefficient adjustment method for Neumann condition in explicit Chebyshev collocation method and its application to compressible Navier- Stokes equations (Q1261371)

The paper consists of two parts. In part 1, a new technique of treating Neumann boundary conditions with an explicit Chebyshev collocation method is developed. Any Neumann boundary condition can be satisfied by adjusting all the Chebyshev coefficients of a solution, which results in a small influence on the solution and its derivatives except at the boundary. Comparisons between the new technique and several traditional ones are made for a one-dimensional advection-diffusion problem, which confirms the superiority of the new technique. The spectral accuracy of the new technique is also demonstrated. In part 2, a Chebyshev collocation code for the compressible Navier-Stokes equations is developed to solve the high-speed flows around a sphere.