Implementation and analysis of a Navier-Stokes algorithm on parallel computers

The results of the implementation of a Navier-Stokes algorithm on three parallel/vector computers are presented. The object of this research is to determine how well, or poorly, a single numerical algorithm would map onto three different architectures. The algorithm is a compact difference scheme for the solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are the following: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally, conclusions are presented

Solving the Cauchy-Riemann equations on parallel computers

Discussed is the implementation of a single algorithm on three parallel-vector computers. The algorithm is a relaxation scheme for the solution of the Cauchy-Riemann equations; a set of coupled first order partial differential equations. The computers were chosen so as to encompass a variety of architectures. They are: the MPP, and SIMD machine with 16K bit serial processors; FLEX/32, an MIMD machine with 20 processors; and CRAY/2, an MIMD machine with four vector processors. The machine architectures are briefly described. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Conclusions are presented

Growth Characteristics Downstream of a Shallow Bump: Computation and Experiment

Measurements of the velocity field created by a shallow bump on a wall revealed that an energy peak in the spanwise spectrum associated with the driver decays and an initially small-amplitude secondary mode rapidly grows with distance downstream of the bump. Linear theories could not provide an explanation for this growing mode. The present Navier-Stokes simulation replicates and confirms the experimental results. Insight into the structure of the flow was obtained from a study of the results of the calculations and is presented

Ocean Warming and Freshening in the Northern Gulf of Alaska

Water column temperatures on the shelf in the northern Gulf of Alaska have increased more than 0.8 degrees C and vertical density stratification has increased since 1970 near Seward, Alaska throughout the 250 m depth. This high latitude marine system has low water temperatures, high rates of precipitation, glacial melting, high wind speeds and high rates of biological productivity. A more than 300 km alongshore shift ( locally westward) of isotherms is suggested. The observations are consistent with a conceptual ocean-atmosphere circulation model that employs coastal freshwater discharge, glacial ablation and wind forcing. Positive regional feedback mechanisms accelerate the discharge and poleward heat flux, leading to even higher temperatures, increased ocean stratification and increased storminess. This warming and ocean freshening will have significant impacts on the atmosphere and marine ecosystems of the Northeast Pacific, Bering Sea, Arctic Ocean and quite possibly global ocean circulation

Continental Runoff and Effects on the North Atlantic Ocean Subtropical Mode Water

Interannual salinity variations in North Atlantic Subtropical Mode Water (STMW) are well known although the cause is less well understood. Attempts to model local salinity variation with local evaporation and precipitation have not been successful and some authors invoke advection of low salinity water as the cause. Examination of the STMW and North American river runoff data suggests that runoff may partly explain the salinity variations. It is known that low salinity water resulting from Mississippi River outflow is transported well past Cape Hatteras. Spearman Rank Correlation analysis and spectra and cross-spectra Fourier correlation analysis both show that river flow is significantly inversely correlated with STMW salinity. This result suggests that North American river flow may have an influence on the salinity of STMW

A mathematical model for the distribution of dissolved silicon in interstitial waters----an analytical approach

A mathematical model for the distribution of dissolved silicon in interstitial waters is studied. This model includes the input flux of particulate silicon, bioturbation, the dissolution of silicon particles, and the diffusion of dissolved silicon in the interstitial water. It is shown that the model reduces to a nonlinear eigenvalue problem. This problem is shown to have only one eigenvalue which is determined by the solution of a simple algebraic equation...

The velocity field created by a shallow bump in a boundary layer

We report the results of measurements of the disturbance velocity field generated in a boundary layer by a shallow three-dimensional bump oscillating at a very low frequency on the surface of a flat plate. Profiles of the mean velocity, the disturbance velocity at the fundamental frequency and at the first harmonic are presented. These profiles were measured both upstream and downstream of the oscillating bump. Measurements of the disturbance velocity were also made at various spanwise and downstream locations at a fixed distance from the boundary of one displacement thickness. Finally, the spanwise spectrum of the disturbances at three locations downstream of the bump are presented

Circulation, Vol. 17, No. 1

Fall 2011 issue of CCPO Circulation featuring article Langmuir Circulations by Dr. Chester E. Groschhttps://digitalcommons.odu.edu/ccpo_circulation/1009/thumbnail.jp

Circulation, Vol. 12, No. 1

Spring 2005 issue of CCPO Circulation featuring article Large Eddy Simulation of Langmuir Circulation in Shallow Water by Dr. Chester Groschhttps://digitalcommons.odu.edu/ccpo_circulation/1018/thumbnail.jp

The Temporally Filtered Navier-Stokes Equations: Propertes of the Residual Stress

Recent interest in the development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, provides the motivation for the present paper. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. This includes the frame-invariance properties of the filtered equations and the resulting residual stress. Causal time-domain filters, parametrized by a temporal filter width 0infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger\u27s equation. Finally, finite filter widths are also considered, and both a priori and a posteriori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted for the model problem