FLUMEN User Manual
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1. U 0E 0 EE Ot Ox O 2 2 2 Numerical Fluxes For a central scheme the fluxes over the cell faces are estimated by the values in the cell midpoints Taking the www fluvial ch 07 2010 6 12 FLUMEN User Manual arithmetic mean of the adjacent points would lead to spurious oscillations in the solution caused by the decoupling of odd and even grid points Hirsch 1988 Therefore different methods have been developed in order to dampen these oscillations Roe 1981 proposed a flux difference splitting scheme FDS which introduces upstream weighting for the flux evaluation Originally developed for the Euler equations the flux difference splitting scheme has been shown to have superior properties for the calculation of viscous flows van Leer et al 1987 The scheme can also be applied to the system of shallow water equations which are essentially hyperbolic Glaister 1988 Using Roe s scheme the numerical flux across a cell face can be written as F F U FU S lAyl U aU 10 ij ij with U and U values at the left and right hand side of the cell face and A Jacobian of the flux vector A OF OU Equation 10 differs from the arithmetic mean by an additional flux that is proportional to the difference AU U U The values U and U can be considered as the states right and left from a discontinuity that leads to the propagation of waves across the cell face Since the solutions are obtained for the linearized2. www fluvial ch 07 2010 5 12 FLUMEN User Manual method equation 1 can be integrated over the ith triangle as aU 5a0 f E 6 d0 5 S U da 5 where A area of the triangle Using the divergence theorem the area integral can be replaced by a line integral around the bounding volume y U da F U ds A S U 6 with I circumference of the triangle The line integral is approximated by the midpoint quadrature rule that is the numerical flux is calculated at the midpoint of the edges Sleigh et al 1995 U 1 Ot 7 LF UO tk UL ER U l l S U 7 with cell edges as defined in the figure below Side ij is the common edge to the triangles associated with U and U l length of this side and F U flux in the outward normal direction evaluated at the midpoint of this edge As the shallow water equations are rotationally invariant the solution of the two dimensional equations can be found in applying locally one dimensional equations with the local coordinate system X y If M D nx and ny are the unit normals in the x and y directions respectively 1 a Gs y ge such that vu n 1 the condition for rotational invariance is Figure 1 Triangular Mesh TF U E TU E U 8 1 0 0 where T 0 n n 0 n n The velocities in the local coordinate system are U u un vn and V u un vn respectively The flux F U over each cell face is found from the solution of the one dimensional equation
3. FLUMEN User Manual FLUMEN User Manual Reusswehr Luzern Projekt EE Keep Mapping Original Query 1 Replot Value Window Examine Grid Alter _ Reusswehr Luzern Variante 8 Flow Velocity m s Bi as CS Ai 3 Feb 03 12 04 fluvial ch www fluvial ch 07 2010 1 12 FLUMEN User Manual Content O NA 3 O O ees eler Dee See deet 3 US erte EE 3 NEE A EE Ee EE A MLN FLOW le WE e EE A A A AR A 4 E dr Eefalt LEE 5 2 1 4 Boundary eeler EE 5 22 NUIMETICAL SOMO EE 5 2 2 1 Finite Volume Method on Toangles ccoo nono nnnnnnnnn nro nn non n nono rn rra nn nnnann rancios 5 2 2 2 Numerical FlUXOS oo 6 2 23 Time RE e 7 3 Usmo RLUMEN o tienta 8 LIO EE 8 KO e A AA AA A AAA 8 Fi SHOP MONS ias 9 FA A Meri at EE 10 3 5 Running FLUMEN in Batch Mode 10 3 6 Generating Quality Messina iii nella 10 A EE NS 12 www fluvial ch 07 2010 2 12 FLUMEN User Manual 1 Introduction 1 1 Overview FLUMEN ELUvial Modelling ENgine is a program for solving the depth averaged shallow water equations on a cell centred unstructured mesh It allows for wet and dry domains sub and supercritical flow conditions and the specification of variable bed topography The main features of FLUMEN are e explicit time integration 1st order e numerical fluxes with flux difference splitting according to Roe 1st order e bed friction with Manning Strickler formula logarithmic friction law or f
4. file can be used to describe many different scenarios Options are invoked with curly brackets option_name input_statement 1 input_statement 2 When calling the program the option must be written following the sign e g flumen input_file_name option_name or if there are several options flumen input_file_name optionl option2 option3 Example We want to run the same model once for the 100 year flood hq100 or the 300 year flood hq300 In the input file we write gt gt boundary hql00 inflow 150 hq300 inflow 220 and start the program with the 100year flood with flumen input_file_name hq100 or for the 300 year flood with flumen input_file_name hq300 It is possible to have options within an other option statement e g hq100 steady inflow 150 unsteady inflow 0 10 1 5 150 3 0 10 and start the program for the 100 year unsteady flood with flumen input_file_name hq100 unsteady Important The option_name must follow directly the open curly bracket without any space in between www fluvial ch 07 2010 9 12 FLUMEN User Manual 3 4 Alternatives Alternatives are an extension of the options described above They are invoked with the character that replaces the logical or Example gt gt boundary hql00 inflow 150 hg300 inflow 220 inflow 50 The inflow in the model is either 150 option hq100 or 220 option hq300 or 50 no
5. keyword is specified e g gt gt source discharge 10 node 9823 gt gt compute start 0 5 end Le gt gt A double arrow without a keyword ends the input reading i e all the input that follows is ignored Lines starting with a slash in the first column are considered as comments and are ignored The keywords are given in the same order as they should appear in the input file If a number has to be specified r denotes a real number and i denotes an integer number String lengths are limited to 32 characters unless explicitely specified 3 2 Includes The syntax allows for include files to divide the model input into separate files Example If you have stored polygon information for the bedlevels on a file called bedlevel inc bedlevel 452 5 129412 457967 129445 457932 129452 458112 129423 458097 bedlevel 445 75 L3041 2 458561 130601 458467 1305924 458512 you can refer to this file in your input file with include bedlevel inc The program then reads from the file bedlevel inc until an end_of file marker or the keyword gt gt appears Then the program continues to read from the input file Important Include files must always start with a keyword This means that is not allowed to split a time table into different pieces www fluvial ch 07 2010 8 12 FLUMEN User Manual 3 3 Options Options allow to specify different parameters in the input file Thus a single input
6. the fluid z bed level and 7 bed shear These equations can be obtained from the Reynolds equations if hydrostatic pressure distribution is assumed The conservative formulation of the equations remains valid in the presence of discontinuous variations of the flow variables such as hydraulic jumps 2 1 2 Friction Factors Bed shear stresses are related to the depth averaged flow velocities as Th uvu v Ty vd v 4 2 f 2 P Cy P oF with u q handv r h The friction factor can be estimated by empirical friction laws Vis A k n Si nig vg e Manning Strickler c with n Manning s value or k k Strickler value 8 f www fluvial ch 07 2010 4 12 FLUMEN User Manual 6 0 with ks equivalent sand roughness A h logarithmic friction law C 2 5 In T 2 1 3 Initial conditions The shallow water equations need initial conditions at the begining of each simulation run There are mainly three different types of initial conditions that can be used in FLUMEN Type Describtion Dry Start The flow variables flow depth and velocity are assumed to be zero over the whole model domain Hot Start FLUMEN reads the flow variables from data stored by a previous run Polygon The flow variables flow depth or water level are defined by closed polygons Table 1 Types of initial conditions in FLUMEN 2 1 4 Boundary Conditions Boundary con
7. E with the ra option e g triangle pqra mesh 1 if the previous mesh is stored in mesh 1 node mesh 1 poly and mesh 1 area 3 Map the mesh points with the DTM data a Load the TIN nodes and elements into Fluviz e g fluviz dtm 1 node b Use the Map option to map the mesh nodes on the TIN surface i e load the node file e g mesh 1 node that needs an update of the z values www fluvial ch 07 2010 11 12 FLUMEN User Manual 4 Literature Beffa C 1994 Praktische L sung der tiefengemittelten Flachwassergleichungen Communication 133 Laboratory of Hydraulics ETH Z rich Hirsch C 1988 Numerical computation of internal and external flows Volume 1 Fundamentals of Numerical Discretization Wiley Chichester Hirsch C 1990 Numerical computation of internal and external flows Volume 2 Computational Methods for Inviscid and Viscous Flows Wiley Chichester Marburger M 1999 Entwicklung eines tiefengemittelten morphodynamischen Fliessgew ssermodells Mitteilungen Heft 8 Wasserbau Universitat Kassel Roe P L 1981 Approximate Riemann solvers parameter vectors and difference schemes J Comp Phys 43 357 372 Shewchuk J R 1995 Triangle Engineering a 2D quality mesh generator and Delaunay Triangulator Carnegie Mellon University Pittsburgh Pennsylvania Sleigh P A Gaskell P H Berzins M Ware J M Wright N G 1995 A reliable an
8. d accurate technique for the modelling of pracitcally occuring open channel flows Proc 9 Int Conf on Numerical Methods in laminar and turbulent flow p 881 892 Pineridge Press Swansea www fluvial ch 07 2010 12 12
9. ditions influence the solution if the flow reaches a model boundary If no boundary conditions are defined FLUMEN assumes non permeable boundaries that is the flow over the boundaries is assumed to be zero In all other cases boundary conditions must be defined by the modeller The number of necessary boundary conditions depend on the flow regime see table below FLUMEN accepts one boundary condition at each boundary At an inflow boundary FLUMEN assumes that the inflow is normal to the model boundary and that the inflow is always subcritical Flow Regime inflow boundary outflow boundary subcritical 2 1 supercritical 3 0 Table 2 Number of boundary conditions At an inflow boundary the discharge must be known keyword inflow FLUMEN distributes the inflow over the boundary edges assuming uniform flow conditions Experience shows that defining the waterlevel at an inflow boundary often leads to an ill conditioned system that does not converge At an outflow boundary it is best to define the slope of the energy head keyword slope or a known waterlevel keyword waterlevel It is also possible to define the ouflow discharge if this is physically sound Time dependent boundary conditions can be defined using time tables see the Reference 2 2 Numerical solution 2 2 1 Finite Volume Method on Triangles FLUMEN uses an unstructured mesh of triangles to discretise the model domain For a cell centred finite volume
10. equations Roe s method defines an approximate Riemann solver Hirsch 1990 It exactly recognises discontinuities and leads to a high resolution of shocks The simplest choice for the variables at the cell faces is setting U U and U U which leads to a scheme whose spatial accuracy is of first order 2 2 3 Time Discretization FLUMEN uses an explicit scheme for solving the differential equation U 2 H U t 11 Se E where the vector H can be considered as the differential space operator prior to discretisation see Equation 1 The simplest choice is the explicit Euler method U U H At 12 where UN and U denote the values on the old and new time level respectively and H H U The accuracy of the Euler method is Ist order in time The explict Euler scheme has to consider the Courant Friedrichs Lewy CFL condition that limits the size of the time step With the CFL numbers in x and y direction At At o lul V gh o lv Vgh 13 Ax Ay where At time step and Ax Ay grid size the CFL condition can be written for TVD schemes as Hirsch 1988 Ta A deiten 14 V2 www fluvial ch 07 2010 7 12 FLUMEN User Manual 3 Using FLUMEN 3 1 Input Syntax The model input is given in free format using predefined keywords Keywords starting with double arrow allow to structure the input The input following a gt gt keyword 1s related to this gt gt keyword until the next gt gt
11. option specified 3 5 Running FLUMEN in Batch Mode FLUMEN can be run in batch mode using script files that allows to start different FLUMEN runs one after the other e g if long jobs has to be done overnight or over the weekend Such a script file could look like this script to run Flumen Flumen flumen in optionl Flumen flumen in option2 Flumen flumen in option3 option4 Script files must be executable and their first character is always The script above does three FLUMEN jobs with the same input file in and different options To avoid that FLUMEN waits for user input to start the simulation it is important that you tell FLUMEN to run in batch mode that is the input file must contain the lines gt gt compute batch_mode 3 6 Generating Quality Meshes There are many different ways to create calculation meshes depending on data quality spatial resolution and structure of the terrain Often it is useful to distinguish between the original terrain model DTM and the calculation mesh that should contain only cells with no small angles The procdure can be divided into three different steps www fluvial ch 07 2010 10 12 FLUMEN User Manual Step To Do Tools Creating the Digital Terrain Model FLUVIZ for data editing and storing data in node and poly DTM from given data e g with formation TRIANGLE for constrained Delaunay triangulation 1 TRIANGLE Creating the calcula
12. tion mesh FLUVIZ for generating the model boundary and important break 2 lines TRIANGLE for quality refinement of the model domain Mapping of the calculation mesh on FLUVIZ for reading in the DTM and mapping the nodes of the 3 the DTM calculation mesh Table 3 Generating a quality mesh in three steps 1 Create a TIN of the digital terrain modell from given data points and break lines a Use Fluviz to load and edit the given data Export data in node and poly format for input into TRIANGLE b Do the meshing in TRIANGLE with the cp option e g triangle cp dtm if the DTM data is stored in the files dhm node and dhm poly see the manual of TRIANGLE for details 2 Create the calculation mesh a Define the boundary of the domain using Fluviz Export the boundary and the break lines in node and poly format b Create a quality refined mesh using TRIANGLE with the q option e g triangle pq mesh if the boundary and break lines are stored in mesh node and mesh poly see the manual of TRIANGLE for details c For local refinement use area files that describe the maximum area for the triangles d To create an area file load the existing mesh into Flumen and edit the values e g of the bedlevels to define the maximum area for each triangle negative values define areas that are not refined Write the nodal values as an area file and give the file the appropriate name e g mesh l area Then start TRIANGL
13. ull log law mobile bed module to account for deposition erosion of sediments and bank failure allows embedded modelling with 1D river branches e adaptive meshes Thanks to the finite volume scheme FLUMEN is extremely robust for mixed sub and supercritical flow regimes Convervation of volume is observed FLUMEN reads meshes as nodes and elements For generating high quality meshes with no small angles the preprocessor FLUVIZ together with the program TRIANGLE Shewchuk 1995 can be used For a detailed describtion of the input syntax see the Reference document 1 2 Applications FLUMEN can be used for almost all flow modelling purposes where the shallow water equation holds e Flood modelling and hazard assessment e Dam Break Analysis e Habitat assessment e Flow analysis e Design of hydraulic structures www fluvial ch 07 2010 3 12 FLUMEN User Manual 2 Basics 2 1 Governing Equations 2 1 1 Flow Equations FLUMEN is based on the depth averaged shallow water equations that can be written in conservation form as OU E GG 4 S 0 1 Ot x dy S with x y horizontal dimensions time and U h g r variable vector with the flow depth h and the components of the specific flow q and r The flux vectors in x and y are q r 2 SE Ep gr pAr oe Gal 2 qr F h 2 and the source vector is 0 OZ T ip a s F Ox p 6 Oy p with g acceleration of gravity p density of
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