Finite Element Method (FEM)

Introduction (3)

The problem analysis prior to the finite element method is divided into the following steps according to [*1]:

Theorie of the Finite Elemente-Methode Application in practice
(1) Discretization of the model area into a finite number of finite elements. Development of a FE-net with river tube and floodplain under consideration of the topographie and the classification of roughness
(2) Derivation of the weighted residual integral or the weak form of the differential equation to investigate and implementation of the finite element approach for the respective equations. internal program process
(3) Combining the elements in a global, algebraic system of equations. internal program process
(4a) Applying boundary and initial conditions to the system of equations. Involvment and approach of all hydrodynamic boundary conditions ( water level-, runoff-hydrograph, W-Q- relations) Choice of a suitable mathematical start solution (lake solution or completely dry)
(4b) Merging area-specific parameters (roughness, eddy viscosity/ turbulence viscosity, fall dry, re-wetting) Election and levying of all necessary hydraulic parameters. Adjustment within the calibration and /or sensitivity analysis
(5) Solving of the system of equations. internal program process, Monitoring of intermediate results
(6) Verification, visualizing and validation of the solution Monitoring, evaluation, visualization (!) and review of the solution. Visualization of complex results.

The monitoring and evaluation of erroneous or as well correct results is only possible with the understanding and knowledge of the "internal program" processes. Only than, if applicable, possible sources of error and erroneous assumptions in the modelling can be made.

The points (1)-(3) will be described in "Method of weighted residuals" and "Vertex connections" by hand of a simple example, while the points (4) and (5) will only be mentioned at the side and in relation to the program RMA2 (or RMA10s).

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Hydrodynamics of Floods



*1 Reddy et al. (1994)



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