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PARMA UNIVERSITY SIMULATIONS OF THE ISOLATED BUILDING TEST CASE F. AURELI, A. MARANZONI & P. MIGNOSA DICATeA, Parma University Parco Area delle Scienze 181/A – 43100 Parma, Italy 3 rd IMPACT Workshop UCL, Louvain-la-Neuve, Belgium November 6 - 7, 2003

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1.Recall of governing equations and description of numerical models 2.Comparison between experimental data and numerical results for the Isolate Building Test Case Validation of the capabilities of 2D FVM numerical codes in modelling rapidly varying flows induced by dam or levee breaks in which the presence of obstacles induces near field effects in the flow field Aim of the study: INTRODUCTION Summary of the presentation: 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be

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with: 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be 2D SHALLOW WATER EQUATIONS with:tensor of fluxes

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Unsplit finite volume discretization of homogeneous advection problem Solution: t where are numerical fluxes j y xi 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be FINITE VOLUMES NUMERICAL MODELS

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3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be SLIC NUMERICAL MODEL (I) Second order accurate in space due to linear extrapolation of variables (MUSCL technique) Second order accurate in time due to t/2 evolution of extrapolated variables maximum upwinding if k = -1

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3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be SLIC NUMERICAL MODEL (II) TVD Property satisfied by the application of Van Leer limiter function Numerical fluxes evaluated by an hybrid centred technique that applies Lax-Friedrichs and Richtmyer methods in two steps (FORCE scheme – Toro, 1997). Explicit, stability satisfied for the application of Courant-Friedrichs-Lewy condition

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3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be WAF NUMERICAL MODEL (I) Second order of accuracy can be achieved by solving the conventional piecewise constant Riemann problem and using the solution averaged over space and time The averaging takes the form of an integral of the flux over some volume The scheme can be extended to two space dimensions via space operator splitting (Strang splitting) N = 3 number of conservation laws, weights expressed as a function of Courant number and wave Speed x - split augmented homogeneous SWE

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3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be WAF NUMERICAL MODEL (II) The conventional piecewise constant Riemann problem is solved using an approximate Riemann solver (HLLC) TVD Property satisfied by the application of well known limiter functions Explicit, stability satisfied for the application of Courant-Friedrichs-Lewy condition m = 1, 2 vector component The exact solution of the Riemann problem in terms of the advected velocity v is: s* = velocity in the star region The third component of the flux is:

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Source term treatment with semi-implicit splitting technique By second-order, implicit, trapezoidal method: SOURCE TERM TREATMENT SOURCE TERM TREATMENT t 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be

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RESULTS (I) 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be Comparison between numerical and experimental water depths waf

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RESULTS (II) RESULTS (II) 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be Comparison between numerical and experimental water depths

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RESULTS (III) RESULTS (III) 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be Comparison between numerical and experimental water depths

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RESULTS(IV) RESULTS(IV) 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be Comparison between numerical and experimental velocities t = 1 sec WAF code on Cartesian domain

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RESULTS(V) RESULTS(V) 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be Comparison between numerical and experimental velocities t = 5 sec WAF code on Cartesian domain

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RESULTS(VI) RESULTS(VI) 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be Comparison between numerical and experimental velocities t = 10 sec WAF code on Cartesian domain

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CONCLUSIONS CONCLUSIONS 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be The numerical water level histories fit satisfactorily the experimental ones apart from Gauge n° 2. This is probably due to nearness of the Gauge to the Hydraulic jump induced by the building. The spatial location of the hydraulic jump is not matched well. At a short distance from Gauge n° 2 the jump is present and the water depths are in better agreement with experimental ones. Moreover in one of the models the description of the building in the Cartesian domain is approximate being the building sides not parallel to the co-ordinate axes. Computed velocities are caught fairly well by the numerical models. Despite not-negligible differences at a local scale, it seems that the proposed 2D models are capable to reproduce in a satisfactory way the overall characteristics of the phenomenon under study.

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ACKNOWLEDGMENTS ACKNOWLEDGMENTS 3 rd IMPACT Workshop - November 6 - 7, 2003 UCL, Louvain-la-Neuve, Be The Authors wish to acknowledge the European Commission, the IMPACT project team, Dr. Eng. S. Soares Frazão and Prof. Yves Zech for providing the experimental data concerning the isolated building test case.

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