A Finite Element Scheme for Shock Capturing Part 3 ppsx
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 7 ppsx
... 31 4 -32 6. Von Neumann, J., and Richtmyer, R. D. (1950). " ;A method for the numerical calculation of hydrodynamic shocks," Journal of Applied Physics 21, 232 - 237 . Walters, R. A. , ... barotropic model," Journal of Physical Oceanography 8, 32 3 -34 3. Steger, J. L., and Warming, R. F. (1981). "Flux vector splitting of the inviscid gas dynamics equations with applications ... Wiley and Sons, New York, 748-754. Leendertse, J. J. (1967). "Aspects of a computational model for long-period water-wave propagation," Memorandum RM 5294-PR, Rand Corporation, Santa...
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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 (19 83) ). 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 ... let's write these nodal values as Chapter 2 Numerical Approach Now substituting Equation 8 yields or, finally so that the shallow-water equations lose energy at the jump, and it...
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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 ... constructed of Plexiglas and simulates a dam break through a horseshoe bend. This is a more general comparison than Case 1. Here the problem is truly 2-D and we now are comparing to hydraulic flume...
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A Finite Element Scheme for Shock Capturing Part 5 pdf
... diamonds. Of particular importance is the arrival time of the shock front. At station 4 the numerical prediction of arrival time using 5 of 1.0 is about 3. 4 sec which appears to be about ... equations can be diagonalized by defining a new variable such that P :A~ P, = A, where Chapter 3 Testing The numerical grid is shown in Figure 23, and contains 698 elements and 811 nodes. ... the channel is 0.1 m and there are five elements across the channel width. For the smooth channel case, Bell, Elliot, and Chaudhry (1992) used a 1-D calculation to estimate the Manning's...
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A Finite Element Scheme for Shock Capturing Part 6 potx
... analysis for a = 112 and for the temporal derivative parameter at of 1.0 and 1.5. We shall compare the relative ampli- tude and relative speed for a single time-step. The parameter for ... 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 ... C and resolution for at = 1.0 and a = 0.5, for small values of C Relative Amplitude 0. Elements per Wavelength Figure 32 . Relative amplitude versus C and resolution for at =...
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A Finite Element Scheme for Shock Capturing ppt
... (1978) or Walters and Carey (19 83) ). 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 ... 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 ... 2-Numerical Approach 13 Advective Dominated Flow 13 The Problem 13 Petrov-Galerkin formulation 14 Shock Capturing 20 Case 1: Analytic Shock Speed 24 Case 2: Dam Break 28 Case...
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CHL - A Finite Element Scheme for Shock Capturing_1 pdf
... 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 Army (R&D). ... of hydraulics as well to complex aerodynamic tlow fields containing shocks. Basic Equations The basic equations that are addressed are the 2-D shallow-water equations given as: Chapter ... conditions. For simple geometries, analytic and flume results are compared with approaches for shock- capturing and shock detection. A trigger mechanism that turns on the capture schemes in...
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CHL - A Finite Element Scheme for Shock Capturing_3 doc
... 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 ... data, 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...
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