A simple and efficient error analysis for multi-step solution of the Navier-Stokes equations

A simple error analysis is used within the context of segregated finite element solution scheme to solve incompressible fluid flow. An error indicator is defined based on the difference between a numerical solution on an original mesh and an approximated solution on a related mesh. This error indicator is based on satisfying the steady-state momentum equations. The advantages of this error indicator are, simplicity of implementation (post-processing step), ability to show regions of high and/or low error, and as the indicator approaches zero the solution approaches convergence. Two examples are chosen for solution; first, the lid-driven cavity problem, followed by the solution of flow over a backward facing step. The solutions are compared to previously published data for validation purposes. It is shown that this rather simple error estimate, when used as a re-meshing guide, can be very effective in obtaining accurate numerical solutions. Copyright © 2002 John Wiley & Sons, Ltd

A comparative study of characteristic-based algorithms for the Maxwell Equations

Characteristic-based finite-difference and finite-volume schemes have been developed for solving the three-dimensional Maxwell equations in the time domain. A detailed eigenvector analysis for the Maxwell equations in a general curvilinear coordinate has also been completed to provide a basic framework for future finite-difference schemes. Although the basic concepts of the two algorithms are identical, the detailed formulations are vastly different for achieving split flux vectors according to the sign of the eigenvalues. A comparative study of these algorithms applied to an oscillating electric dipole is carried out to assess their relative merit for further development. In spherical coordinates, second-order windward numerical simulations of the radiating phenomenon are closely comparable in terms of accuracy and efficiency. These methods also demonstrate an ability to suppress reflected waves from the truncated boundary by a simple compatibility condition. © 1996 Academic Press, Inc

Adaptive, multi-level numerical scheme for the solution of the Navier-Stokes equations

A simple error analysis is used within the context of segregated finite element solution scheme to solve incompressible fluid flow. An error indicator is defined based on the difference between a numerical solution on an original mesh and an approximated solution on a related mesh. This error indicator is based on satisfying the steady state momentum equations. The advantages of this error indicator are: simplicity of implementation; ability to show regions of high and/or low error; and as the indicator approaches zero the solution approaches convergence. Two examples are chosen for solution; first, the lid-driven cavity problem is solved, followed by the solution of flow over a backward facing step. The solutions are compared to previously published data for validation purposes. It is shown that this rather simple error estimate, when used as a re-meshing guide, can be very effective in obtaining accurate numerical solutions

Coupling of a nonlinear finite element structural method with a navier-stokes solver

A new three-dimensional viscous aeroelastic solver is developed in the present work. A well validated full Navier-Stokes code is coupled with a nonlinear finite element plate model. Implicit coupling between the CFD and structural solvers is achieved using a subiteration approach. Computations of several benchmark static and dynamic plate problems are used to validate the finite element portion of the code. This coupled aeroelastic scheme is then applied to the problem of threedimensional panel flutter. Inviscid and viscous supersonic results match previous computations using the same aerodynamic method coupled with a finite difference structural solver. For the case of subsonic flow, multiple solutions consisting of static, upward and downward deflections of the panel are discussed. The particular solution obtained is shown to be sensitive to the cavity pressure specified underneath the panel

A comparative study of numerical algorithms for computational electromagnetics

Characteristic-based finite-difference and finite-volume schemes have been developed for solving the three-dimensional Maxwell equations in the time domain. Although the basic concept of the two algorithms is identical, the detailed formulation is vastly different for achieving split fluxes according to the sign of the eigenvalues. A comparative study of these algorithms applied to an oscillating electric dipole is carried out to determine the most efficient numerical procedure for future applications. On spherical coordinates, second-order windward numerical simulations of the radiating phenomenon are closely comparable in terms of accuracy and efficiency. These methods also demonstrate an ability to suppress reflected waves from the truncated boundary. The third-order upwind biased finite-volume scheme reveals a superior performance in stability properties and higher numerical accuracy. © 25th AIAA Plasmadynamics and Lasers Conference

Numerical study of U-tube passive anti-rolling tanks

The accurate prediction of the stabilizing effect of U-tube anti-roll tanks has long been of great interest to naval architects. Traditionally, there are two approaches in this area. The majority of the previous work done is limited to model testing only some investigations are performed using approximate mathematical models. In this paper, Computational Fluid Dynamics (CFD) techniques are applied to study U-tube tanks. The Finite Element Method (FEM) is used to formulate the problem and the segregated method is utilized to solve the discretized Navier-Stokes Equations [1] in a local coordinate system. Gauss numerical integration is used to evaluate complicated integrals resulting from the coordinate transformations. Also the moment calculation is based on the finite element concept. The application of the numerical technique herein are restricted to the study of U-tube anti-roll tanks when the ship roll motion is small, slow, and sinusoidal. Moreover, the results correspond to Reynolds numbers corresponding to scale model tests. The goal of this paper is to introduce the Computational Fluid Dynamics technique to the study of stabilizing effect of U-tube anti-roll tanks. It is found that Computational Fluid Dynamics is an effective approach to study the stabilizing effect of U-tube tanks. In order to get more accurate and general results from the CFD study, turbulence models should be used in the case of finite amplitude and finite frequency roll motion [30]. At the same time, numerical techniques to deal with the free surface can also be included in future investigations

Finite-element analysis of conjugate heat transfer in axisymmetric pipe flows

A Galerkin-type finite-element approach was used to study the effect of two-dimensional wall conduction on laminar convective heat transfer inside pipe flows. This conjugate heat transfer problem was studied for cases in which the external surface of the pipe is subjected to constant wall heat flux and constant wall temperature conditions. The wall conduction effects were found to be more significant for low Peclet number flows than their high Peclet number counterparts. The extent of preheating extends as far as 22 radii and 7 radii for constant wall heat flux and constant wall temperature conditions, respectively. © 1988 Taylor 8 Francis Group, LLC

Coupling of a nonlinear finite element structural method with a Navier-Stokes solver

A new three-dimensional viscous aeroelastic solver is developed in the present work. A well validated full Navier-Stokes code is coupled with a nonlinear finite element plate model. Implicit coupling between the computational fluid dynamics and structural solvers is achieved using a subiteration approach. Computations of several benchmark static and dynamic plate problems are used to validate the finite element portion of the code. This coupled aeroelastic scheme is then applied to the problem of three-dimensional panel flutter. Inviscid and viscous supersonic results match previous computations using the same aerodynamic method coupled with a finite difference structural solver. For the case of subsonic flow, multiple solutions consisting of static, upward and downward deflections of the panel are discussed. The particular solution obtained is shown to be sensitive to the cavity pressure specified underneath the panel. © 2003 Published by Elsevier Science Ltd

A proposed hardware in the loop gimbal platform that supports an applied graduate controls course

This paper investigates the premises of a hardware-in-the-loop (HIL) platform that supports a graduate controls course and consolidates the lecture and laboratory. Hardware in the loop has been used in industry and is now an integral part of academia. The course being considered at the Arkansas Tech University (ATU) is unique due to a concentrated effort on the emphasis of the software/ hardware interfaces specific to engineering applications, and avoids pure theoretical modeling and development in its course content. Based upon further investigations forthcoming, this hardware/laboratory development at ATU being proposed focuses on opportunities for further course development and student interaction in the classroom environment. The course development also coincides with the interests of industry and supports a graduate program that is limited in coure offerings. © 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved

A study of the non-parabolic hydrodynamic modelling of a sub-micrometre n\u3csup\u3e+\u3c/sup\u3e-n-n\u3csup\u3e+\u3c/sup\u3e device

The common assumptions for closure of the first three moment equations with non-parabolic band structure have led to many inconsistencies associated with the electron temperature, effective mass and heat flux. The assumptions are involved in the heat flux based on the Fourier law and in the electron temperature determined from the average kinetic and drift energies. The inconsistencies resulting from these assumptions are studied and illustrated for electrons in silicon with a non-parabolic energy band. A simple alternative by means of which to avoid the inconsistent assumptions and to truncate the hierarchy of the hydrodynamic equations with non-parabolic band structure is proposed. Instead of using the Fourier-law heat flux to close the hydrodynamic equations, the energy flux is separated into fluxes carried by average and random velocities. The proposed model and a Fourier-law-based hydrodynamic model, together with the Monte Carlo method, are applied to a silicon sub-micrometre n+-n-n+ diode with a non-parabolic band at various applied voltages. Effects on electron transport in the sub-micrometre device resulting from the assumptions of the Fourier-law heat flux and the electron temperature determined from the average kinetic and drift energies are investigated