R. M. M. Mattheij

Convergence analysis of the local defect correction method for diffusion equations

Summary.This paper is concerned with the convergence analysis of the local defect correction (LDC) method for diffusion equations. We derive a general expression for the iteration matrix of the method. We consider the model problem of Poissons equation on the unit square and use standard five-point finite difference discretizations on uniform grids. It is shown via both an upper bound for the norm of the iteration matrix and numerical experiments, that the rate of convergence of the LDC method is proportional to H2 with H the grid size of the global coarse grid.

Discretization of the stationary convection-diffusion-reaction equation

A finite volume method for the convection-diffusion-reaction equation is presented, which is a model equation in combustion theory. This method is combined with an exponential scheme for the computation of the fluxes. We prove that the numerical fluxes are second-order accurate, uniformly in the local Peclet numbers.

Acoustic modes in a duct with slowly varying impedance and non-uniform mean flow and temperature

Noise from the auxiliary power unit (APU) is becoming an increasingly important aircraft design constraint because of the noise exposure during ground operations (ramp-noise). Reduction of noise may be achieved by liners in the exhaust duct. In this paper, we will consider the propagation of sound through the APU exhaust duct, which is typically straight with an axially varying liner depth, a non-uniform mean flow and strong temperature gradients. We present a solution in the form of slowly varying modes of WKB type for the acoustic pressure field inside a duct with an impedance that is continuously varying in the axial direction. In cross-wise direction each WKB mode is given by eigenfunction-type solutions of the Pridmore-Brown equation. A new numerical approach based on a standard implementation of a collocation method supplemented by a path-following procedure is presented to solve this equation. We compare the results of the slowly-varying solution with a solution based on mode-matching between axial segments with constant impedance.

LDC with compact FD schemes for convection-diffusion equations

We discuss an algorithm for convection-diffusion equations with high activity areas which combines the Local Defect Correction technique with high order compact finite difference schemes.