B. K. Muite

A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems

In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral space preconditioned Chebyshev tau, real space Chebyshev integration and spectral space Chebyshev integration methods are compared in the L^2 and W^2^,^2 norms when solving linear fourth order boundary value problems; and in the L^~([0,T];L^2) and L^~([0,T];W^2^,^2) norms when solving initial boundary value problems. We find that the best Chebyshev method to use for high resolution computations of solutions to initial boundary value problems is the spectral space Chebyshev integration method which uses sparse matrix operations and has a computational cost comparable to Fourier spectral discretization.

The effects of a counter-current interstitial flow on a discharging hourglass

This work experimentally investigates the effects of an interstitial fluid on the discharge of granular material within an hourglass. The experiments include observations of the flow patterns, measurements of the discharge rates, and pressure variations for a range of different fluid viscosities, particle densities and diameters, and hourglass geometries. The results are classified into three regimes: (i) granular flows with negligible interstitial fluid effects; (ii) flows affected by the presence of the interstitial fluid; and (iii) a no-flow region in which particles arch across the orifice and do not discharge. Within the fluid-affected region, the flows were visually classified as lubricated and air-coupled flows, oscillatory flows, channeling flows in which the flow preferentially rises along the sidewalls, and fluidized flows in which the upward flow suspends the particles. The discharge rates depends on the Archimedes number, the ratio of the effective hopper diameter to the particle diameter, and hourglass geometry. The hopper-discharge experiments, as well as experiments found in the literature, demonstrate that the presence of the interstitial fluid is important when the nondimensional ratio (N) of the single-particle terminal velocity to the hopper discharge velocity is less than 10. Flow ceased in all experiments in which the particle diameter was greater than 25% of the effective hopper diameter regardless of the interstitial fluid.

Performance of FORTRAN and C GPU Extensions for a Benchmark Suite of Fourier Pseudospectral Algorithms

A comparison of PGI Open ACC, FORTRAN CUDA, and Nvidia CUDA pseudospectral methods on a single GPU and GCC FORTRAN on single and multiple CPU cores is reported. The GPU implementations use CuFFT and the CPU implementations use FFTW. Porting pre-existing FORTRAN codes to utilize a GPUs is efficient and easy to implement with Open ACC and CUDA FORTRAN. Example programs are provided.

Liquid Filled Hourglasses: A Study of Interstitial Fluid Effects on the Kinetic Behavior of Granular Materials

Experimental measurements of discharge rate and observations of flow pattern were made for spherical, monosized particles in a liquid- filled, hourglass shaped container. Different combinations of fluid properties, solid properties and vessel geometry exhibited a range of flow patterns that are described as lubricated, fluidized, oscillatory, or localized channeling discharges. A Bagnold number is used to present the discharge rate and flow regime results.