Hans Johnston

Comparison of turbulent thermal convection between conditions of constant temperature and constant flux.

We report the results of high-resolution direct numerical simulations of two-dimensional Rayleigh-Bénard convection for Rayleigh numbers up to Ra=10;{10} in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we considered the extreme cases of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law Nu approximately 0.138xRa;{0.285} with a scaling exponent indistinguishable from 2/7=0.2857... above Ra=10;{7}. The overall flow dynamics for both scenarios, in particular, the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers.

A Cartesian treecode for screened coulomb interactions

A treecode algorithm is presented for evaluating electrostatic potentials in a charged particle system undergoing screened Coulomb interactions in 3D. The method uses a far-field Taylor expansion in Cartesian coordinates to compute particle-cluster interactions. The Taylor coefficients are evaluated using new recurrence relations which permit efficient computation of high order approximations. Two types of clusters are considered, uniform cubes and adapted rectangular boxes. The treecode error, CPU time and memory usage are reported and compared with direct summation for randomly distributed particles inside a cube, on the surface of a sphere and on an 8-sphere configuration. For a given order of Taylor approximation, the treecode CPU time scales as O ( N log N ) and the memory usage scales as O ( N ) , where N is the number of particles. Results show that the treecode is well suited for non-homogeneous particle distributions as in the sphere and 8-sphere test cases.

A Fourth Order Scheme for Incompressible Boussinesq Equations

A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation. The method is especially suitable for moderate to large Reynolds number flows. The momentum equation is discretized by a compact fourth order scheme with the no-slip boundary condition enforced using a local vorticity boundary condition. Fourth order long-stencil discretizations are used for the temperature transport equation with one-sided extrapolation applied near the boundary. The time stepping scheme for both equations is classical fourth order Runge–Kutta. The method is highly efficient. The main computation consists of the solution of two Poisson-like equations at each Runge–Kutta time stage for which standard FFT based fast Poisson solvers are used. An example of Lorenz flow is presented, in which the full fourth order accuracy is checked. The numerical simulation of a strong shear flow induced by a temperature jump, is resolved by two perfectly matching resolutions. Additionally, we present benchmark quality simulations of a differentially-heated cavity problem. This flow was the focus of a special session at the first MIT conference on Computational Fluid and Solid Mechanics in June 2001.

Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study

We introduce a continuous (downscaling) data assimilation algorithm for the 2D Bénard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to constrain the model. Our numerical results indicate that the approximate solution of the algorithm is converging to the unknown reference solution (vorticity and temperature) corresponding to the measurements of the 2D Bénard convection problem when only spatial coarse-grain measurements of vorticity are assimilated. Moreover, this convergence is realized using data which is much more coarse than the resolution needed to satisfy rigorous analytical estimates.

A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier---Stokes Equations

A spectral collocation scheme for the three-dimensional incompressible

A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux boundaries

({\varvec{u}},p)

High-Rayleigh-number convection in a fluid-saturated porous layer

(u,p) formulation of the Navier–Stokes equations, in domains