Adaptivity with moving grids

118 C. J. Budd, W. Huang and R. D. Russell
T (t =1.1867) Mesh (t =1.1867)
T (t =1.2275) Mesh (t =1.2275)
T (t =1.2321) Mesh (t =1.2321)
Figure 5.10. The contour plot of the temperature T (where white
represents 2.2 and black represents 1) and the moving meshes are
shown at various times.
conditions are
u| t=0 = T | t=0 =1, in Ω,
u| ∂Ω = T | ∂Ω =1, for t>0
and the physical parameters are set to be Le =0.9,α =1,δ = 20, and
R = 5. A resulting calculation obtained with an MMPDE finite element
method as described in Section 3 (with details in Cao et al. (1999a)) is
shown in Figure 5.10.
5.5. Convection-driven problems in meteorology
A system of interest to meteorologists is the Eady problem, which describes
the evolution of (localized) extra-tropical (mid-latitude) cyclones. The Eady
problem is a two-dimensional reduction of the Euler equations describing
the (incompressible) air velocity (u, w) and pressure P in the (x, z)-plane,
where x ∈ [−L, L] is a horizontal coordinate along lines of constant latitude,