Multi-dimensional hybrid Fourier continuation-WENO solvers for conservation laws

We introduce a multi-dimensional point-wise multi-domain hybrid Fourier-Continuation/WENO technique (FC-WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and essentially dispersionless, spectral, solution away from discontinuities, as well as mild CFL constraints for explicit time stepping schemes. The hybrid scheme conjugates the expensive, shock-capturing WENO method in small regions containing discontinuities with the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [A. Harten, Adaptive multiresolution schemes for shock computations, J. Comput. Phys. 115 (1994) 319-338]. We consider a WENO scheme of formal order nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws are investigated for problems with both smooth and non-smooth solutions. The Euler equations for gas dynamics are solved for the Mach 3 and Mach 1.25 shock wave interaction with a small, plain, oblique entropy wave using the hybrid FC-WENO, the pure WENO and the hybrid central difference-WENO (CD-WENO) schemes. We demonstrate considerable computational advantages of the new FC-based method over the two alternatives. Moreover, in solving a challenging two-dimensional Richtmyer-Meshkov instability (RMI), the hybrid solver results in seven-fold speedup over the pure WENO scheme. Thanks to the multi-domain formulation of the solver, the scheme is straightforwardly implemented on parallel processors using message passing interface as well as on Graphics Processing Units (GPUs) using CUDA programming language. The performance of the solver on parallel CPUs yields almost perfect scaling, illustrating the minimal communication requirements of the multi-domain strategy. For the same RMI test, the hybrid computations on a single GPU, in double precision arithmetics, displays five- to six-fold speedup over the hybrid computations on a single CPU. The relative speedup of the hybrid computation over the WENO computations on GPUs is similar to that on CPUs, demonstrating the advantage of hybrid schemes technique on both CPUs and GPUs. (C) 2013 Elsevier Inc. All rights reserved

Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC-WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319-338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC-WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems. (C) 2011 Elsevier Inc. All rights reserved

Efficient High-Order Discontinuous Galerkin Methods for Fluid Flow Simulations

Khosro Shahbazi of Brown University presented a lecture on February 22, 2010 at 2:00 pm in room 1116 E of the Klaus Advanced Computing Building on the Georgia Tech campus.Runtime: 49:09 minute

VOLUME TRACKING ON TRIANGULAR MESHES

ABSTRACT This paper investigates a volume tracking algorithm on triangular meshes, associated with modeling free surface flow and multi phase flow on complex geometry. The volume tracking algorithm is divided into two main tasks. First, a piecewise linear reconstructing the interface is used to approximate the interface at each interfacial cell with a segment line. The convergence study of this approach reveals first order accuracy in reproducing a circular material distribution. Second, a Lagrangian time integration accompanied by a full remap is carried out in order to advect volume material in time. A circular material distribution is tested under simple translation and rotation. Visualization of results shows that the circular shape is conserved while first order accuracy is observed. INTRODUCTION Volume tracking algorithms are important for modeling flows with discontinuous interfaces such as free surface and multi-phase flow. Developed in the mid-1970, volume tracking has just recently been approached with rigorous mathematical formalism. The need to achieve second order accuracy lead to piecewise linear volume tracking algorithm which approximates the interface with a segment line through each interfacial cell. Basically a piecewise linear volume tracking algorithm consist

Numerical investigation of the effectiveness of radon control measures in cave mines

Ventilation is one of the radon control measures in an underground working environment. However, the dynamics related to the cave mining methods particularly in block/panel cave mines, complicate the design of effective ventilation system, and implementation. Events such as hang ups (in the drawbells), leakage from old workings, and changes in cave porosity lead to differing response of an existing ventilation designs. However, it is difficult to investigate these conditions at the mine or with a laboratory scale study. Therefore, this study develops a discrete model to investigate the impact of different radon control measures in cave mines using computational fluid dynamics techniques. We considered two ventilation conditions for a fully developed cave: with and without the undercut ventilation. For each of the two conditions, we studied four parameters: airflow distribution through the production drifts, radon distribution through the production drifts, the effect of increasing airflow on radon concentration, and the effect of a cave top negative pressure on radon distribution. The results show that: the undercut ventilation significantly increases the radon concentration in the production drift; the growth of radon concentration through the production drift is nonlinear (oscillating pattern); maintaining a negative pressure on top of the cave is more effective at mitigating radon exposure, when the undercut ventilation is active; and increase in air volume flow rate decreases radon concentration in most regions, however, there might be regions with significant radon accumulation due to pressure variation across the drifts. These findings provide vital information for designing an effective ventilation system and for proactive implementation of radon control measures in cave mines. Keywords: Radon gas, Underground mining, Panel cave mines, Broken rocks, Computational fluid dynamics (CFD), Porous media, Cave mining metho

Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC–WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319–338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC–WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems

Comparison of the efficiency of mesoporous silicas as absorbents for removing naphthalene from contaminated water

Mesoporous silicas MCM-48 and SBA-15 were synthesized and characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Fourier transform infrared (FTIR) spectroscopy. Adsorption capacity of two mesoporous silica for removing naphthalene from waste water was determined. The results indicate that under similar conditions, SBA-15 had a better adsorption capacity than MCM-48. In this context, SBA-15 was modified using 3-aminopropyltrimethoxysilane and the effect of contact time, adsorbent dose, solution pH and concentration of naphthalene was investigated in batch adsorption systems. Solution pH appeared to be a key factor affecting the adsorption of naphthalene by NH2-SBA-15. The adsorption experiments revealed that a higher percentage of up to 79.3% of naphthalene was adsorbed in highly acidic media (pH of 2). The equilibrium data were analyzed using Langmuir and Freundlich isotherms and nonlinear regression analysis. This revealed that based on the correlation coefficient (R2 = 0.979) the Langmuir model provided the best fit to the results. The adsorption kinetic was determined using the pseudo-first order, pseudo-second order and Elovich kinetic models. Of the kinetics models tested, the pseudo-first-order equation provided the best fit to the results (R2 = 0.991) of the absorption of naphthalene by the adsorbent