Multiple-grid Technique Research Articles

Conceptual analogy between the water hammer phenomenon in free-surface and pressurized-pipe flows

ABSTRACT The water hammer phenomenon, commonly acknowledged in pressurized pipe-flows is relevant to various water distribution systems. This phenomenon constitutes a major concern for hydraulic researchers and designer, given the dramatic consequences of this phenomenon on hydraulic structures and human life. This study aimed at expanding research on the water hammer waves in the free-surface flow framework. The main objective was to address a comprehensive simulation of the free-surface wave behavior caused by the abrupt closure of sluice-gate in prismatic open channel. The one-dimensional Saint-Venant equations embedding the Boussinesq add-on was used to predict the free-surface wave behavior; which was discretized using the (2–4)-dissipative scheme. Results evidenced the analogy between the water hammer wave behavior in free-surface and pressurized pipe flows. Furthermore, results illustrated that the water hammer maneuver produced a sudden depth rise, about three times of the normal depth value in the cross section adjacent to the gate. From a computational point of view, the proposed solver provided simplicity and accuracy attributes in simulating shock-waves in free-surface-flow. This solver also consumed low computational time compared with the conventional or multiple grid technique – based Finite Element Algorithm.

Investigating the unidirectional flow behavior in trapezoidal open-channel

ABSTRACT This paper applies a Multiple-Grid technique -based Finite Element algorithm to predict the free-surface wave behavior in trapezoidal open-channel. This technique aims to limit the computational time consumed in the standard Finite Element procedure. The spatial integration of the flow model uses a Discontinuous Galerkin approach; while the time integration employs a Semi Implicit Euler method. The test case relates to the transient flow regime arising from the failure of a hydraulic power plant placed at the downstream extremity of an open-channel. Results show better performances of the Multiple-Grid technique compared to the conventional one in terms of consumed computational time criterion. Besides, the results obtained by the proposed algorithm illustrate close agreement with those obtained by the Finite Difference Method -based alternative algorithm.

Analysis of electromagnetic radiation from a video output amplifier inside a monitor by using FDTD method

The finite-difference time-domain (FDTD) method is used to analyze the electromagnetic compatibility and interference (EMC and EMI) problems due to the electromagnetic radiation from a video output amplifier located inside a computer monitor. The multiple grid technique is implemented in the FDTD method to improve the computational efficiency. The video output amplifier is modeled by a rectangular iron container with an equivalent dipole antenna located at the center of one opened wall facing the cathode-ray-tube (CRT). The coupled electric fields inside and outside the monitor are calculated. It is found that higher values of coupled electric fields occur near the monitor screen. It is also found that the coupled electric fields outside the CRT region drop sharply in amplitude. Simulation results of coupled electric fields at a distance of 3 m from the monitor screen also comply with the FCC regulations. Calculation results also agree with the experimental data for coupled electric fields outside the monitor screen at a measured distance of 3 m.

DECOMPOSITION AND PARALLELIZATION STRATEGIES FOR ADAPTIVE GRID-EMBEDDING TECHNIQUES

SUMMARY A two and three-dimensional adaptive-grid procedure for the solution to fluid dynamic problems is presented. This procedure uses grid-embedding (h-refinement) to automatically refine the grid in regions of high gradients and high truncation error. With this adaptation approach, solutions are obtained with a guaranteed level of accuracy using minimum computer resources. For the solution of steady flows, a multiple-grid technique is used to allow disturbance waves to pass through regions of disparate grid spacing and to accelerate convergence. Domain decomposition and computer parallelization techniques are utilized to allow the solution procedure to be executed efficiently on parallel computer platforms. A discussion of these techniques along with a general description of the adaptive grid-embedding procedure is given. Results are provided demonstrating the accuracy and efficiency of the present procedure on a parallel computer.

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.

Multiple grid solution of the open channel flow equations using a marching finite-volume method

A multi-grid algorithm has been developed to accelerate the convergence solution of the open channel flow equations to obtain the steady flow. The scheme is constructed by combining the multiple-grid technique with a new marching finite-volume numerical solution. In the multi-grid application the corrections to the fine grid points are transferred to a coarse grid to maintain the low truncation errors associated with a fine level of discretizations. Distribution formulae are then used to propagate the changes onto selected coarser grid points. After applying interpolation to coarse grid corrections, the flow properties at every grid point of the fine mesh are updated. The channel flow will be assumed to be 2D, steady and viscous with wind and Coriolis forces neglected. The flow is also assumed to be fully mixed in the vertical direction. The general technique used is a combination of the finite-element and finite-difference methods. The governing PDE are transformed into an equivalent system applied over a square-grid network. Convergence histories are presented for supercritical flows as well as for super-critical flows with hydraulic jump presence. Numerical results indicate that substantial computational savings for the solution accuracy can be achieved.

Prediction of compressible, laminar viscous flows using a time-marching control volume and multiple-grid technique

On presente une nouvelle technique numerique de prevision des ecoulements laminaires par la resolution des equations de Navier-Stokes dependantes du temps. La methode utilisee est precise au second ordre en espace et temps. La technique est appliquee a differentes geometries internes et externes