A Finite Element Scheme for Shock Capturing Part 2 pptx
CHL - A Finite Element Scheme for Shock Capturing_1 pdf
... Version - 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 ... transitions and preserve the Rankine-Hugoniot conditions. For simple geometries, analytic and flume results are compared with approaches for shock- capturing and shock detection. A trigger mechanism ... Hydrodynamics. 3. Shock (Mechanics) - Mathematical models. 4. Finite element method. I. United States. Assistant Secretary of the Army (Research, Development and Acquisi- tion) 11. U.S. Army...
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CHL - A Finite Element Scheme for Shock Capturing_3 doc
... the comparison is to actual flume data. The comparisons are made to the water surface heights and timing of the shock passage. The final case is a steady-state comparison to flume data reported ... 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 ... roots are non-negative and so node-to-node oscillations are damped. In 2-D we follow a similar procedure. The particular approach to numerical simulation chosen here is a Petrov- Galerkin finite...
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CHL - A Finite Element Scheme for Shock Capturing_4 pdf
... go to smaller grid spacing. Values of C, less than 1 appear to lag the analytic shock and Cs greater than 1 leads the analytic shock. With the largest C, the calculated shock speed ... arrival is 3.55 sec which is about 0.1 sec late (3 percent). At station 6 both flume and numerical model arrival times for at of 1.0 were about 4.3 sec and for slation 8 the numerical ... depth and Ah is the analytic depth difference across the shock, 0.1 m. The error was as small as was detectable by the technique for measurement of speed at AX = 0.4 m so there was no...
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CHL - A Finite Element Scheme for Shock Capturing_5 potx
... reach the smallest time-step. Again if we are within the shock at a depth where there is an upstream propagating wave (subcritical), is there a Courant number C that has a relative speed greater ... indicates nondimensional quantities and o as a subscript indicates a constant, and These equations can be diagonalized by defining a new variable such that P :A~ P, = A, where Chapter ... amplitude portrait shows substantial damping for larger C and for the shorter wavelengths (or alternatively the poorer resolution). The large damp- ing at a wavelength of 2Ax is important,...
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CHL - A Finite Element Scheme for Shock Capturing_6 potx
... Wiley and Sons, New York, 74 8-7 54. Leendertse, J. J. (1967). "Aspects of a computational model for long-period water-wave propagation," Memorandum RM 5294-PR, Rand Corporation, Santa ... Experiment Station aulics Laboratory Halls Ferry Road, Vicksburg, MS 3918 0-6 199 Technical Report HL-9 3-1 2 sistant Secretary of the Army (R&D) shington, DC 20315 vailable from National Technical ... model will have application in supercriti- cal as well as subcritical channels, and transitions between regimes. The model can determine the water surface heights along channels and around bridges,...
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A Finite Element Scheme for Shock Capturing ppt
... 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 ... the comparison is to actual flume data. The comparisons are made to the water surface heights and timing of the shock passage. The final case is a steady-state comparison to flume data reported ... indicates nondimensional quantities and o as a subscript indicates a constant, and These equations can be diagonalized by defining a new variable such that P :A~ P, = A, where Chapter...
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A Finite Element Scheme for Shock Capturing Part 1 potx
... analytic and flume results are compared with approaches for shock- capturing and shock detection. A trigger mechanism that turns on the capture schemes in the vicinity of shocks and the characteristic ... Laboratory Independent Research Program A Finite Element Scheme for Shock Capturing by R. C. Berger, Jr. Hydraulics Laboratory U.S. Army Corps of Engineers Waterways Experiment Station ... Petrov-Galerkin formulation 14 Shock Capturing 20 Case 1: Analytic Shock Speed 24 Case 2: Dam Break 28 Case 3: 2-D Lateral Transition 40 Discussion 43 References 55 ...
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A Finite Element Scheme for Shock Capturing Part 2 pptx
... (1978) or Walters and Carey (1983)). Typically, these are chosen as depth as an elemental constant and velocity as linear, or depth linear and velocity as a quadratic. This approach effectively ... Momentum relation. Again assuming constant density, the balance of momentum and force may be written as (in the direction of the normal to the shock) and taking the limit as GI and Q2 shrink ... Calerkin approach and an approach to develop a Petrov-Galerkin test function. Chapter 2 Numerical Approach Figure 1. Definition of terms for a moving hydraulic jump Uo = velocity at section...
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A Finite Element Scheme for Shock Capturing Part 3 ppsx
... 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 ... the comparison is to actual flume data. The comparisons are made to the water surface heights and timing of the shock passage. The final case is a steady-state comparison to flume data reported ... for which discrepancy will be due to the hydrostatic assumption made in the shallow- water equations. Instead we have a direct way of evaluating the numerical scheme alone. As spatial and...
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A Finite Element Scheme for Shock Capturing Part 4 docx
... speed at AX = 0 .4 m so there was no need to go to smaller grid spacing. Values of C, less than 1 appear to lag the analytic shock and Cs greater than 1 leads the analytic shock. ... defined as MlAh. Here h is the depth and Ah is the analytic depth difference across the shock, 0.1 m. The error was as small as was detectable by the technique for measurement of speed at ... to the analytic speed. Figures 14- 16 and 17-19 are the center-line profile histories for at = 1.5 and for AX = 0 .4 and 0.8 m, respectively. It is apparent that the lower dissipation from...
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A Finite Element Scheme for Shock Capturing Part 5 pdf
... a general 2-D setting. Chapter 3 Testing 0 .5 0 0 .5 1.0 1 .5 2.0 2 .5 3.0 3 .5 4.0 4 .5 5.0 5. 5 6.0 6 .5 7.0 DISTANCE FROM CONTRACTION, FT 0 .5 0 0 .5 1.0 1 .5 2.0 2 .5 3.0 3 .5 4.0 4 .5 5.0 5. 5 ... 4 .5 5.0 5. 5 Time, sec A, is the diagonal matrix of eigenvalues and Po and P-: are composed of the eigenvectors (and are arbitrary). With the substitution of Equation 55 into 54 and ... indicates nondimensional quantities and o as a subscript indicates a constant, and These equations can be diagonalized by defining a new variable such that P :A~ P, = A, where Chapter...
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A Finite Element Scheme for Shock Capturing Part 6 potx
... the spatial node location. We now present the results of this analysis for a = 112 and for the temporal derivative parameter at of 1.0 and 1.5. We shall compare the relative ampli- ... Figures 6- 11 for Case 1, analytic shock case, we must remember that C, is the Courant number based on shock speed, whereas C is based on the perturbation wave speed. If we consider a wave moving ... note that generally we get a sharp front with no undershoot until we reach the smallest time-step. Again if we are within the shock at a depth where there is an upstream propagating wave (subcritical),...
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A Finite Element Scheme for Shock Capturing Part 7 ppsx
... Wiley and Sons, New York, 74 8 -75 4. Leendertse, J. J. (19 67) . "Aspects of a computational model for long-period water-wave propagation," Memorandum RM 5294-PR, Rand Corporation, Santa ... Monica, CA. Moretti, G. (1 979 ). "The A- scheme, " Computers in Fluids 7( 3), 191-205. Platzman, G. W. (1 978 ). "Normal modes of the world ocean; Part 1, Design of a finite element ... Von Neumann, J., and Richtmyer, R. D. (1950). " ;A method for the numerical calculation of hydrodynamic shocks," Journal of Applied Physics 21, 232- 2 37. Walters, R. A. , and Carey,...
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A Practical Guide for Health Researchers - part 2 pptx
... trial versionwww.adultpdf.com 26 A practical guide for health researchers 3 .2 Selection of a field for research3 .2. 1 Categories of health research Health research has been broadly defined as ... of a characteristic. An analytical study is an observational study that describes associations and analyses them for possible cause and effect.An observational study may be cross-sectional ... research design. The researcher has to select the appropriate design for the particular study. All types of research design have a place, and all have advantages and disadvantages. But not all...
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Finite Element Analysis - Thermomechanics of Solids Part 2 pptx
... )(((TEN 22 ) TEN 22 TEN 22( ) TEN 22 TEN 22 ) TEN 22 T(()(() ((()(CCUC CCU C===abcnn))) 2 2 Ua CbnTEN 2 22= ()Un 2 Un 2 Un 2 Un 2 Un 2 Un 2 Un 2 Un 2 Un 2 Un 2 Un 2 ′=′ABTGCG0749_Frame_C 02 ... CT1TT 22 2 T 2 T 2 T)()(,)()(,) () (,)() (,) ()(,)() (,) ()TEN b aTEN a b TEN b aTEN a b TEN b aTEN a b TEN b ajilkik jl ik jlki jl ki jlik lj ik lj 22 22 22 22 22 22 22 ======= 22 T 2 TT 2 TT333T3TABCBA ... ì[]AT1 23 .[] .= 22 Aij ija= 22 1 2 2 2 3A []. = ìì 2 ii i() . = ì ì2T TTAA A()[ ].= ìì 2T TTAnAnAdV ) dS dS([].31 2 230+=III,I tr I tr tr I 12 22 31 2 ==− =( ) [...
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