galerkin finite element scheme

... problem within the finite elements method by the development of a single test function that reflects the speed of fluid transport (the SUPG scheme, Streamline llpwind Eetrov -Galerkin) to be applied ... http://www.simpopdf.com Waterways Experiment Station Cataloging-in-Publication Data Berger, Rutherford C A finite element scheme for shock capturing / by R.C Berger, Jr., ; prepared for Assistant Secretary of the ... Laboratory Independent Research (ILIR) Program The funding was providing by ILIR work unit "Finite Element Scheme for Shock Capturing." Dr R C Berger, Jr., ED, performed the work and prepared this...

Ngày tải lên: 20/06/2014, 17:20

... is precisely what our scheme does Therefore, the Petrov -Galerkin scheme we are using to address advection-dominated flow is a good scheme for shock capturing as well The scheme dissipates energy ... chosen here is a PetrovGalerkin finite element method applied to the shallow-water equations For the shallow-water equations in conservative form (Equation I), the Petrov -Galerkin test function ... variation for each element and flags those elements which have a high variation as needing a larger value of a for shock capturing Note that this would work even in a Galerkin scheme since this...

Ngày tải lên: 20/06/2014, 17:20

... is in the region of the contraction near the dam breach The basic element length in the channel is 0.1 m and there are five elements across the channel width For the smooth channel case, Bell, ... Unregistered Version - http://www.simpopdf.com The numerical grid is shown in Figure 23, and contains 698 elements and 811 nodes This grid was reached by increasing the resolution until the results no longer...

Ngày tải lên: 20/06/2014, 17:20

... 1.5 in Figures 35-42 The condition a = is, in fact, the Galerkin case since the Petrov -Galerkin contribution is included through a The Galerkin approach is shown to contain a steadystate spurious ... spaced elements laterally across the channel and 24 over the length of the transition The model limits were extended some 40 ft (12.192 m) The total number of nodes was 1661 with 1500 elements ... http://www.simpopdf.com Relative Speed - Elements per Wavelength 10 Figure 31 Relative speed versus C and resolution for at = 1.0 and a = 0.5, for small values of C Relative Amplitude Elements per Wavelength...

Ngày tải lên: 20/06/2014, 17:20

... dissipative Galerkin scheme for open-channel flow," by N D Katopodes, Jountal of Hydraulic Engineering, ASCE, 111(4), 1200-1204 Gabutti, B (1983) "On two upwind finite different schemes for hyperbolic ... (1982) "A theoretical framework for Petrov -Galerkin methods with discontinuous weighting functions: Applications to the streamline-upwind procedures." Finite Elements in Fluids R H Gallagher, et al., ... Monica, CA Moretti, G (1979) "The A -scheme, " Computers in Fluids 7(3), 191-205 Platzman, G W (1978) "Normal modes of the world ocean; Part 1, Design of a finite element barotropic model," Journal...

Ngày tải lên: 20/06/2014, 17:20

... is precisely what our scheme does Therefore, the Petrov -Galerkin scheme we are using to address advection-dominated flow is a good scheme for shock capturing as well The scheme dissipates energy ... chosen here is a PetrovGalerkin finite element method applied to the shallow-water equations For the shallow-water equations in conservative form (Equation I), the Petrov -Galerkin test function ... problem within the finite elements method by the development of a single test function that reflects the speed of fluid transport (the SUPG scheme, Streamline llpwind Eetrov -Galerkin) to be applied...

Ngày tải lên: 27/06/2014, 14:20

... problem within the finite elements method by the development of a single test function that reflects the speed of fluid transport (the SUPG scheme, Streamline llpwind Eetrov -Galerkin) to be applied ... 1993 Waterways Experiment Station Cataloging-in-Publication Data Berger, Rutherford C A finite element scheme for shock capturing / by R.C Berger, Jr., ; prepared for Assistant Secretary of the ... Laboratory Independent Research (ILIR) Program The funding was providing by ILIR work unit "Finite Element Scheme for Shock Capturing." Dr R C Berger, Jr., ED, performed the work and prepared this...

Ngày tải lên: 07/08/2014, 10:20

... equation is enforced Finite elements are a subset of the weighted residual method Here one looks at the solution of a differential equation in a weighted average sense In the Galerkin approach the ... a numerical scheme is driven by two related difficulties: numerically modeling highly advective flow and the capturing of shocks This chapter discusses the problem with advection schemes generally ... problem with the Calerkin approach and an approach to develop a Petrov -Galerkin test function Chapter Numerical Approach Petrov -Galerkin formulation First we will illustrate the problem that discrete...

Ngày tải lên: 07/08/2014, 10:20

... is precisely what our scheme does Therefore, the Petrov -Galerkin scheme we are using to address advection-dominated flow is a good scheme for shock capturing as well The scheme dissipates energy ... chosen here is a PetrovGalerkin finite element method applied to the shallow-water equations For the shallow-water equations in conservative form (Equation I), the Petrov -Galerkin test function ... variation for each element and flags those elements which have a high variation as needing a larger value of a for shock capturing Note that this would work even in a Galerkin scheme since this...

Ngày tải lên: 07/08/2014, 10:20

... the shock becomes steeper The shock is fairly consistently spread over three or four elements; and so as the element size is reduced, the resulting shock is steeper The x-t slope of the shock indicates ... the analytic shock speed and the ratio of time-step length to element length A C, value of indicates that the shock should move element length in time-step Figures 12 and 13 show the error in ... = 0.4 and 0.8 m, respectively It is apparent that the lower dissipation from this second-order scheme allows an oscillation which is most notable upstream of the jump for larger values of C,...

Ngày tải lên: 07/08/2014, 10:20

... spaced elements laterally across the channel and 24 over the length of the transition The model limits were extended some 40 ft (12.192 m) The total number of nodes was 1661 with 1500 elements ... 3.5 sec The nodes are delineated by the symbols along the lines The overshoot of the second-order scheme and the damping of the first-order is obvious Again, it is probable that the overshoot is...

Ngày tải lên: 07/08/2014, 10:20

... 1.5 in Figures 35-42 The condition a = is, in fact, the Galerkin case since the Petrov -Galerkin contribution is included through a The Galerkin approach is shown to contain a steadystate spurious ... Testing Relative Speed - Elements per Wavelength 10 Figure 31 Relative speed versus C and resolution for at = 1.0 and a = 0.5, for small values of C Relative Amplitude Elements per Wavelength ... = 0.5 Chapter Testing Relative Speed Elements per Wavelength Figure 33 Relative speed versus C and resolution for at = 1.5 and a = 0.5 Relative Speed Elements per Wavelength 10 Figure 34 Relative...

Ngày tải lên: 07/08/2014, 10:20

... (1982) "A theoretical framework for Petrov -Galerkin methods with discontinuous weighting functions: Applications to the streamline-upwind procedures." Finite Elements in Fluids R H Gallagher, et al., ... Monica, CA Moretti, G (1979) "The A -scheme, " Computers in Fluids 7(3), 191-205 Platzman, G W (1978) "Normal modes of the world ocean; Part 1, Design of a finite element barotropic model," Journal ... of Computers and Fluih, 11(1), 51-68 References Form Approved REPORT DOCUMENTATION PAGE Finite Element Scheme for Shock Capturing Army Engineer Waterways Experiment Station aulics Laboratory...

Ngày tải lên: 07/08/2014, 10:20

... Modelling of Visco-Acoustic Waves with Finite- Difference and Finite- Element Discontinuous Galerkin Methods 127 The second issue concerns the numerical scheme used to discretize the wave equation ... Visco-Acoustic Waves with Finite- Difference and Finite- Element Discontinuous Galerkin Methods 145 f f where u is the wavefield vector of components u = (p,vx,vy,vz) i is the index of the element f in an ... discontinuous Galerkin methods, J Comput Phys 227(3): 2044–2072 www.intechopen.com Frequency-Domain Numerical Modelling of Visco-Acoustic Waves with Finite- Difference and Finite- Element Discontinuous Galerkin...

Ngày tải lên: 27/07/2014, 23:25

... Géradin/D.Rixen: Mechanical Vibrations, Wiley, 1994 C.T.Sun, Y.P.LU: Vibration Damping of Structural Elements, Prentice Hall Englewood Cliffs, NJ 07632, 1984 Kelley , S.G: Fundamentals of Mechanical...

Ngày tải lên: 09/04/2013, 12:58

... Notes: Introduction to Finite Element Method Chapter Introduction Solution Techniques for Linear Systems of Equations •Gauss elimination methods •Iterative methods Positive Definite Matrix A square ... BC) (associative) © 1998 Yijun Liu, University of Cincinnati Lecture Notes: Introduction to Finite Element Method Chapter Introduction Transpose of a Matrix If A = [aij], then the transpose of ...  = ad − bc c d  © 1998 Yijun Liu, University of Cincinnati Lecture Notes: Introduction to Finite Element Method Chapter Introduction and a11 a12 det a21 a22   a31 a32 a13  a23  = a11a22a33...

Ngày tải lên: 17/10/2013, 11:15

... to Finite Element Method Chapter Introduction Types of Finite Elements 1-D (Line) Element (Spring, truss, beam, pipe, etc.) 2-D (Plane) Element (Membrane, plate, shell, etc.) 3-D (Solid) Element ... v Lecture Notes: Introduction to Finite Element Method Chapter Introduction Chapter Introduction I Basic Concepts The finite element method (FEM), or finite element analysis (FEA), is based on ... geometrically simple pieces (elements) © 1997-2003 Yijun Liu, University of Cincinnati Lecture Notes: Introduction to Finite Element Method Chapter Introduction Why Finite Element Method? Design analysis:...

Ngày tải lên: 23/10/2013, 15:46

... stiffness matrix for e=1:numberElements; % elementDof: element degrees of freedom (Dof) elementDof=elementNodes(e,:) ; stiffness(elementDof,elementDof)= stiffness(elementDof,elementDof)+[1 -1;-1 1]; ... element, in a vector elementDof For example, for element 1, elementDof =[1,2], for element 2, elementDof =[2 3] and so on % elementDof: element degrees of freedom (Dof) elementDof=elementNodes(e,:) ... matrix for e=1:p1.numberElements; % elementDof: element degrees of freedom (Dof) elementDof=p1.elementNodes(e,:) ; p1.stiffness(elementDof,elementDof)= p1.stiffness(elementDof,elementDof)+[1 -1;-1...

Ngày tải lên: 06/01/2014, 22:09

... 8-nodded elements 221 FIGURE 8.5 Eight elements finite element approximation with two 8-nodded elements 222 FIGURE 8.6 Estimation of rainfall using finite element ... programming the finite element method In addition, MATLAB will allow the reader to focus on the finite element method rather than on the programming details Programming the finite element method ... result with the finite element method Remark: The preceding sections illustrate the steps required in a finite element analysis As can be noticed, even for a small number of elements (in this...

Ngày tải lên: 08/01/2014, 12:58

... Finite Elements matrices Using this factorized formulation, a novel algorithm is presented It corresponds to a reformulation of the iterative algorithm of S.M Rump [9] adapted to the Finite Elements ... [−10.2, −9.8] [29.4, 30.6] (31) Interval Computations Applied to FEM If we consider the elementary Finite Element matrix of the Euler Bernoulli theory [24], the static matrix equation of the problem ... thickness, clearance ), or physical ones (Young’s Modulus ) Then the matrices given by the Finite Element theory are interval matrices, and the problem is generally (static problems, frequency...

Ngày tải lên: 12/01/2014, 21:45