Analysis of Compact Schemes for Diffusion Terms with Variable Properties

Kledson Flávio Silveira Santiago¹; Leonardo Santos de Brito Alves¹

¹ Universidade Federal Fluminense

doi:10.20906/CPS/COB-2015-1797

Resumo

This study presents a numerical investigation on the treatment of diffusive terms with variable properties. A theoretical analysis illustrates the accuracy loss phenomenon related to many known schemes, where spatial resolution tests of fourth order accurate centered schemes. For this formulation, conservative and non-conservative compact finite difference were employed. They are compared to different finite difference methods. These comparisons are based on several criteria: numerical stability of the reference time-marching scheme, spatial error distribution, spatial accuracy order, computational cost and spectral resolution. A new fourth-order formulation is proposed in order to overcome the difficulties associated with different schemes analyzed here.

Palavras-chave: spatial resolution; diffusive terms; spectral resolution; compact schemes