A comparison of high performance fortran and message passing parallelization of a geophysical fluid model

MPDATA: A Finite-Difference Solver for Geophysical Flows

“…Note that the stability of the first pass ensures that of the second pass, since |U | ≤ 1 ⇒ −1 ≤ |U | − U 2 ≤ 1 and the assumed nonnegativity of , together with the positivity of the donor-cell scheme assure |A (1) i+1/2 | ≤ 1 ∀i. For illustration, Table 1 summarizes a series of elementary advection tests (uniform translation of a Gaussian pulse) for a range of spatial resolutions and Courant numbers.…”

“…The superscript (1) shows that it is the first approximation to subtracting the error. Inside the derivative in (6), the diffusive flux in the second term of (4) is multiplied by a factor of over -i.e., by unity.…”

“…where A (1) and B (1) are numerical estimates at the particular edge. For example, on the right edge of a cell…”

“…To compensate for the error between the donor cell solution (1) and a second-order accurate solution n+1 , we use the error (6) estimated at time level n + 1. A first-order accurate estimate of the pseudo velocity (nondimensionalized for convenience) is…”

“…MPDATA has also been used as an interpolator [27] in a class of semi-Lagrangian fluid models congruent to the Eulerian MPDATA models [28,31], as well as a remapper in arbitrary LagrangianEulerian (ALE) simulations of high-speed flows [3,12]. Several MPDATA-based fluid models have been implemented on massively parallel platforms [1,2,16], demonstrating that the local iterative character of the schemes is well-suited to distributed memory architectures.…”