finite volume scheme for compressible multiphase flows

... where n : Manning coefficient for the bed roughness τ x = ρC f u u , C f = 2.2 Numerical scheme The finite volume formulation imposes conservation laws in a control volume Integration of Eq (1) ... Godunov-type scheme for this purpose According to the Godunov-type scheme, the numerical fluxes at a cell interface could be obtained by solving a local Riemann problem at the interface The Godunov scheme ... recorded for comparing with the experimental data Initial Condition Similar to Synolakis's (1987) 0.5 (m) For the numerical simulation, the initial solitary wave is simulated by the solitary wave formula...

Ngày tải lên: 22/03/2014, 12:20

... solutions over the cells, Uin xi U (tn , x) dx (2.4) Ci A nite volume conservative scheme for solving (1.8) is a formula of the form Uin+1 Uin + t (Fi+1/2 Fi1/2 ) = 0, xi (2.5) telling how ... minimal property required for a scheme to ensure that we approximate the desired equation For a conservative scheme, we dene it as follows Denition 2.1 We say that the scheme (2.5)(2.6) is consistent ... property for a scheme to preserve an invariant domain is an important issue of stability, as can be easily understood In particular, the occurrence of negative values for density of for internal...

Ngày tải lên: 23/03/2014, 01:20

... 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) 61 p : ill ; ... (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 report under the general supervision ... the Euler equations with the depth substituted for density and dropping the energy equation This equation set is ideal for testing numerical schemes for the Euler equations The model developed can...

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 ... simulation 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 ... what happens in a numerical scheme in which the depth is approximated as CO;i.e., it is continuous We are onIy enforcing mass and momentum, but we are implicitly enforcing energy conservation...

Ngày tải lên: 20/06/2014, 17:20

... reasonable The test results for stations 4, and are shown in Figures 24-26 Here the time-history of the water elevation is shown for the inside and outside of the channel for both the numerical model ... than for the flume This is roughly 1-2 percent fast For of 1.5 the time of arrival is 3.55 sec which is about 0.1 sec late (3 percent) At station both flume and numerical model arrival times for ... Figure 20 Error in model shock speed with grid refinement for = 1.5 Figure 21 Relative error in model shock speed with grid refinement for at = 1.5 Chapter Testing Simpo PDF Merge and Split Unregistered...

Ngày tải lên: 20/06/2014, 17:20

... this analysis for a = 112 and for the temporal derivative parameter at of 1.0 and 1.5 We shall compare the relative amplitude and relative speed for a single time-step The parameter for relative ... less than for the first-order case The relative speed is better but not so dramatic as the improvement in amplitude An interesting point is that the relative speed for N = is nonzero for lower ... below C values of 0.5 As with q = 1, for very low C the numerical relative speed is greater than the analytic Therefore, we would expect to have an undershoot for small time-steps It should become...

Ngày tải lên: 20/06/2014, 17:20

... upwind finite different schemes for hyperbolic equations in non-conservative form," Coinputers and Fluids 11(3), 207-230 Hicks, F E., and Steffler, P M (1992) "Characteristic dissipative Galerkin scheme ... REPORT DOCUMENTATION PAGE Finite Element Scheme for Shock Capturing Army Engineer Waterways Experiment Station aulics Laboratory Halls Ferry Road, Vicksburg, MS 39180-6199 Form Approved OMB NO 0704-0188 ... is large for short wavelengths, thus enforcing energy loss through the hydraulic jump, unlike a nondissipative technique used on C" representation of depth, which will implicitly enforce energy...

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 ... 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) 61 p : ill ; ... the Euler equations with the depth substituted for density and dropping the energy equation This equation set is ideal for testing numerical schemes for the Euler equations The model developed can...

Ngày tải lên: 27/06/2014, 14:20

... 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) 61 p : ill ; ... (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 report under the general supervision ... the Euler equations with the depth substituted for density and dropping the energy equation This equation set is ideal for testing numerical schemes for the Euler equations The model developed can...

Ngày tải lên: 07/08/2014, 10:20

... happens Therefore any small perturbations are swept toward, and are engulfed in the shock Shock relations in 2-D Previous sections derive the shock relations in l-D and are important for understanding ... performed separately; and then by letting the width about the shock go to zero, we derive the mass and momentum relationship across the jump in the direction n Figure Definition of terms for ... as the shock is approached in subdomain n2 For an arbitrary segment T , to preserve the equation, the integrand itself must satisfy the equation, therefore Chapter Introduction where which states...

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 ... simulation 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 ... what happens in a numerical scheme in which the depth is approximated as CO;i.e., it is continuous We are onIy enforcing mass and momentum, but we are implicitly enforcing energy conservation...

Ngày tải lên: 07/08/2014, 10:20

... 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 this second-order scheme allows an oscillation which is ... the associated Figures 20 and 21 for error in calculated shock speed and relative error in calculated speed The error is actually worse than for the first-order scheme This is due primarily to ... Figure 20 Error in model shock speed with grid refinement for = 1.5 Figure 21 Relative error in model shock speed with grid refinement for at = 1.5 Chapter Testing Chapter Testing ...

Ngày tải lên: 07/08/2014, 10:20

... Figure 24 Flume and numerical model depth histories for station Chapter Testing ' I " ' ~ Figure 25 Flume and numerical model depth histories for station Chapter Testing Station 8, Flume T i e ... elevations, comparison of temporal representation, for time of 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 ... dam These distance measurements are in terms of the center-line distance The two conditions are for cq of 1.0 and 1.5, i.e., first- and second-order temporal derivative Channel Center Line Distance,...

Ngày tải lên: 07/08/2014, 10:20

... resolution for at = 1.0 and a = 0.5 Figure 30 Relative speed versus C and resolution for at = 1.0 and a = 0.5 Chapter Testing In comparison to the results we have shown in Figures 6-11 for Case ... less than for the first-order case The relative speed is better but not so dramatic as the improvement in amplitude An interesting point is that the relative speed for N = is nonzero for lower ... below C values of 0.5 As with q = 1, for very low C the numerical relative speed is greater than the analytic Therefore, we would expect to have an undershoot for small time-steps It should become...

Ngày tải lên: 07/08/2014, 10:20

... equations," 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 ... "Aspects of a computational model for long-period water-wave propagation," Memorandum RM 5294-PR, Rand Corporation, Santa Monica, CA Moretti, G (1979) "The A -scheme, " Computers in Fluids 7(3), ... "A method for the numerical calculation of hydrodynamic shocks," Journal of Applied Physics 21, 232237 Walters, R A., and Carey, G F (1983) "Analysis of spurious oscillation modes for the shallow...

Ngày tải lên: 07/08/2014, 10:20

... (2.9) Discontinuous Galerkin Method Formulation of DG method The finite difference schemes [21, 30, 31] solve Eqn (2.1) in the difference form For the Finite Volume schemes [23, 15], Eqn (2.13) is integrated ... discretization for a scheme to be formally higher order accurate Since the DG scheme can have an arbitrary order of accuracy in space, here we use a temporal discretization scheme that can be formulated ... actual simulation The Finite Volume (FV) schemes are a class of numerical methods which are constructed by applying the integral form of the NS equations on the control volume With the application...

Ngày tải lên: 09/09/2015, 18:52

... short for volume pixel, are the smallest entity for a 3D volumetric dataset Volumetric datasets are created by stacking series of 2D images, thus creating depth and combining adjacent pixels to form ... Varying PMMA Cement Volume 44 Effects of Varying PMMA Spatial Distribution 46 2.7.3 Computational Biomechanics for Vertebroplasty Research 48 Finite Volume Method and Finite Element ... for Intraosseous Flow Simulation 148 Generating the Vertebral Body Finite Volume Mesh 148 Grouping of Finite Volumes for Automatic Permeabilty Assignment 150 Smoothening of the Voxel-based...

Ngày tải lên: 13/09/2015, 21:18

... Applications For studying the equilibrium problem, f is usually assumed to satisfy the following conditions: A1 f x, x for all x ∈ C; A2 f is monotone, that is, f x, y f y, x ≤ for all x, y ∈ C; A3 for ... smooth if ρE τ > 0, for all τ > 0, and E is called uniformly smooth if and only if limτ → ρE τ /τ A Banach space E is said to be strictly convex if x y /2 < for all x, y ∈ E with for any x y and ... quasi-φ-nonexpansive mapping for each i ∈ {1, 2, , N}, αn,0 , {αn,1 }, , {αn,N } are real sequences in 0, satisfying N αn,j for each n ≥ and j lim infn → ∞ αn,0 αn,i > for each i ∈ {1, 2, ...

Ngày tải lên: 21/06/2014, 05:20

... k For each component k governed by the Euler equations, multiplying mass, momentum and energy equations by Xk , respectively, and performing volume average for the resulting expressions and for ... 97 Chapter High-resolution Methods for Barotropic Two-fluid and Barotropic-nonbarotropic Two-fluid Flows 4.1 112 PPM for Barotropic-nonbarotropic Two-fluid Flows 113 4.1.1 4.1.2 Governing ... 6.24 Density iso-surfaces for krypton sphere, Ma = 1.2 185 6.25 Density contours for krypton sphere, Ma = 1.2 186 6.26 Volume fraction iso-surfaces for krypton sphere, Ma =...

Ngày tải lên: 14/09/2015, 08:44

... Models for Inviscid Compressible Flows 3.1 37 40 Looking for a simple equilibrium distribution function for inviscid compressible flows 40 Deriving lattice models for ... LB models for compressible flows 1.3.1 Current LB models for incompressible thermal flows 1.3.2 Current LB models for compressible flows ... 5.1 Finite volume method and flux evaluation for compressible Euler equations 101 5.2 LBM-based flux solver 104 5.3 Numerical validation for one dimensional FV-LBM scheme...

Ngày tải lên: 14/09/2015, 14:01