Abstract
This paper investigates the geophysically relevant problem of thermal convection in a Maxwell medium. The case of convection in a 2-dimensional cavity heated from below is solved numerically for infinite Prandtl number and constant material parameters. Within a finite difference context, different approximation schemes for the advective terms in the material equations are explored. Using an upwind approximation, solutions for an upper convected Maxwell model up to Deborah numbers De ≈ 1.0 are possible, where the vigour of the convective flow is reduced to approximately 50% of its Newtonian equivalent. At this De the normal stress pattern seems to become singular at the boundaries. For De < 0.5 it is shown that the results are mainly controlled by the choice of the free parameters, a, of a Johnson-Segalman model.
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