HyFlux2: a numerical model for the impact assessment of severe inundation scenario to chemical facilities and downstream environment by Giovanni Franchello, Elisabeth Krausmann EUR 23354 EN - 2008 HyFlux2: a numerical model for the impact assessment of severe inundation scenario to chemical facilities and downstream environment by Giovanni Franchello, Elisabeth Krausmann EUR 23354 EN - 2008 The Institute for the Protection and Security of the Citizen provides research-based, systems- oriented support to EU policies so as to protect the citizen against economic and technological risk. The Institute maintains and develops its expertise and networks in information, communication, space and engineering technologies in support of its mission. The strong cross- fertilisation between its nuclear and non-nuclear activities strengthens the expertise it can bring to the benefit of customers in both domains. 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It can be accessed through the Europa server http://europa.eu/ JRC 36005 EUR 23354 EN ISSN 1018-5593 Luxembourg: Office for Official Publications of the European Communities © European Communities, 2008 Reproduction is authorised provided the source is acknowledged Printed in Italy 1 – Introduction Failures of dams and water-retaining structures continue to occur. After some days of high rainfall, the explosive failure of the Malpasset concrete dam in France in 1959 led to 433 casualties and eventually prompted the introduction of dam-safety legislation into France. In October 1963, 2000 people died in Italy when a landslide fell into the Vajont reservoir creating a flood wave some 250m high that overtopped the dam and flooded the downstream valley. In Spain 1998, the Los Frailes tailings dam failure (Aznalcóllar, Spain) caused immense ecological damage from the release of polluted sediments into the Guadiamar river and Donana National Parc. Similarly, in Romania 2000, Baia Mare, the failure of a mine tailings dam due to heavy precipitation and snowmelt released lethal quantities of cyanide into the river system, thereby polluting the environment and a major source of drinking water for both Romania and Hungary [1]. After the Indian Ocean Tsunami in 2004, field investigations highlighted that the tsunami consisted of high- velocity "surges" rushing inland for kilometres, followed by a series of incoming "bores" advancing in the seawater-inundated coastal plains [2]. These surges exhibited similar characteristics with dam-break wave events. The 2004 tsunami resulted in about 300000 casualties and damage is estimated at over 10 billion $US [3]. Of critical importance for engineering design are the flow velocities and flow depths, which may reach 10-30 m/s and 2-25 metres respectively above the natural bed level. The aim of the HyFlux2 model, recently developed within the European Commission Joint Research Centre’s (JRC) MAHB-NEDIES project [4], is to predict tsunami surges on coastal plains, as well as dam-break waves in flood plains. The model can be used to: a) define inundation hazard maps with maximum water depth and wave arrival time for risk management and emergency planning b) quantify the impact forces from the flow on civil-engineering structures, providing guidelines for civil- engineering safety design c) test innovative mitigation and protection methods that can shelter evacuation sites and critical infrastructure This supports the JRC’s activities on protecting the citizens from technological or natural disasters by trying to prevent them from happening or by mitigating their consequences. In particular, a recent activity at the JRC aims at understanding the underlying mechanisms of natural-hazard triggered technological accidents (so-called Natech disasters) and the HyFlux2 model will supplement the ongoing assessment of the flooding risk of chemical installations storing and/or processing hazardous materials [5]. This paper gives a description of the HyFlux2 model and applies it to a selected 2D test example, the Malpasset dam-break case study. 2 – The HyFlux2 Model The basic ingredient of the HyFlux2 model for solving the shallow water equations is a 2D finite volume Approximate Riemann Solver, with a high-resolution Flux Vector Splitting technique and implicit treatment of the source terms, which makes the model able to capture local discontinuities - like shock waves - and reduces numerical diffusion and unphysical viscosity effects which dominate in all finite-difference methods. The numerical model has been validated with respect to different numerical 1D test cases and comparisons with the exact solution of the Riemann problem are presented in paper [6]. 2.1 – The Shallow Water Equations The 2D system of the shallow water equation solved by the HyFlux2 model can be conveniently written as follows: ∂U r + Δ ⋅FC = (1) ∂t r where U is the conservative vector, FFF= {x, y } is the flux vector and C the source vector. ⎧ ⎫ ⎧ ⎫ ⎧ h ⎫ ⎧ hv ⎫ hvy ⎪ q ⎪ ⎪ ⎪ x ⎪ ⎪ , ⎪ 2 2 ⎪ , F = hv v , ⎪ ∂z ⎪ U = ⎨hvx ⎬ Fx =⎨hvx + gh 2/ ⎬ y ⎨ y x ⎬ C =⎨ fvy − gh()+ S fx ⎬ 2 2 ∂x ⎪hv ⎪ ⎪ hv v ⎪ ⎪hv+ gh 2/ ⎪ ⎪ ⎪ ⎩ y ⎭ ⎩ x y ⎭ ⎩ y ⎭ ⎪−fv − gh⎜⎛∂z + S ⎟⎞⎪ ⎩ x ⎝ ∂y fy ⎠⎭ 3 → In the above notation, h signifies the water depth, the horizontal velocity of the fluid, z the vertical v = {vx, v y } coordinate of the bottom (or bed), η the elevation of the free surface, g the gravitational acceleration (opposite r to the z direction), f = 2ω sinθ the Coriolis parameter and S f denotes the bottom friction that can be expressed by the well known Manning formula → 2 2 2 n vx+ v y = SS, = v, v (2) S f {}fx fy 4 {x y } h 3 where n is an empirical roughness coefficient for the water – called also Manning coefficient - which is in the order of 0.01÷0.1, depending on the surface roughness (see Fig 2.1). The quantity q is a “lateral flow” which could be the rainfall or other external sources. Fig. 2.1 - Schematic of the coordinates and variables of the shallow water model 2.2 – Numerical Method For the numerical solution scheme, the governing Eq. (1) is transformed into a finite volume and time approximation (Fig. 2.2). In a Cartesian space domain, indices i,j indicate the control volumes or cells at column i and row j and n the time-step level. The conservative vector U i, j , assigned to the centre of the cell, at time level n+1, is given by Δt ⎛ n n ⎞ Δt ⎛ n n ⎞ n+1 n * * * * n+1 (3) UUi, j =i, j − ⎜()()Fx i+ ,2/1 j − Fx i− ,2/1 j ⎟ − ⎜()()Fy i, j+ 1/ 2 − Fy i, j− 1/ 2 ⎟ +Ci, j Δ t Δxi ⎝ ⎠ Δy j ⎝ ⎠ Note that the source vector is evaluated at the “new” time step n +1, in order to handle the “stiffness” of the * * * * source terms. The vectors (),(),(),()FFFFx i+ ,2/1 j x i− ,2/1 j y i, j+ 1/ 2 y i, j− 1/ 2 are the interface fluxes calculated at each x- and y-directions. Fig. 2.2 – Finite volume discretisation of Cartesian domain. A typical cell has four interface boundaries. For each interface a Left (L) and a Right (R) cell can be identified. The space domain is transformed into so called 1D dam break problems - or Riemann problems - at each cell interface (Fig. 2.3). The conservative equation (3) is the natural extension of the one-dimensional conservative equation and is completely determined once the interface fluxes are calculated [7] 4 Fig. 2.3 – Linearized Riemann Solver for each cell interface in x,y directions. The solution of the 1D Riemann problem for each cell interface is the numerical flux F * , called also “Godunov “ flux, calculated from the corresponding fluxes FFLR, in the “left” and “right” cell as FF+ FF− F * = LR + G* LR (4) 2 2 with GG* = sub in case of sub-critical flow and GG* = sup in case of super-critical flow. ⎧ v ⎫ − η 1 0 ⎪ c c ⎪ ⎧sign(λ3 ) 0 0 ⎫ 2 ⎪ 2 ⎪ sup ⎪ ⎪ sub ⎪c− vη vη ⎪ (5) G = 0 G = ⎨ 0 sign()λ3 0 ⎬ ⎨ c c ⎬ ⎪ ⎪ ⎪ ⎪ 0 0 sign()λ 0 0 sign()λ3 ⎪ 3 ⎪ ⎩ ⎭ ⎩⎪ ⎭⎪ More details about the methodologies used to obtain Eq. (4), called also Flux Vector Splitting, introduced by H.Steadtke et al. to model two-phase flows, implemented by G.Franchello for the shallow water flows, can be found in [6,8,9]. The quantities λ1 =vη − c, λ2 = vη + c, λ3 = vη are the characteristic velocities and c= gh is the celerity of the gravitational wave. The flux in the 1D Riemann problem is defined by 2 2 F= { hvη, hv η + gh,2/ hvη v τ }. (6) The velocity (vη, v τ ) takes the place of (vx, v y ) for the x-direction and of (vy, v x ) for the y-direction. Note that only in the case of super-critical flow - like in the donor cell technique - the flux from the upstream cell → is taken. The coefficient of the G* matrix - the velocity and the celerity c - are computed by an v = (vη, v τ ) arithmetic average of these quantities at the “left” and “right” sides of the cell interface.