Main Steps Developing Your Own Simulator

Transcription

1 Main Steps Developing Your Own Simulator Peter Böhm, inutech GmbH

2 The Diffpack Vision s = F t ( v, s, t ) arbitrary PDE, ODE, or or other numerical problem [ κ u] f in = Ω u = g on Ω Diffpack Kernel + = own Diffpack Toolboxes (further extensions) own solver

3 Convection-Diffusion Equation - Model Diffusion Term Governing equation: Convection Term ( k u( x, ) + v u( x, = f ( x,, x, y Ω u( x, k v f ( x, Temperature distribution Diffusion Constant Velocity Heat Source

4 Convection-Diffusion Equation - Boundary Γ 1 Γ 1 Ω Γ2 Γ 1 Boundary Conditions: u ( x, = 0, x, y Γ 1 essential conditions k u( x, = α u( x, + α U s, x, y Γ n mixed conditions 2 U s Environmental temperature

5 Convection-Diffusion Equation Weak Formulation I Galerkin: uˆ ( x, = m j= 1 u j N j Approx. of exact Solution N j Shape Functions R( uˆ; x, ( k u ˆ( x, ) + v uˆ( x, f ( x, = Residuum Ω R( uˆ; x, Ni dω= 0, i = 1,..., m

6 Convection-Diffusion Equation Weak Formulation II Galerkin: m [ k u ˆ( x, ) + v uˆ( x, f ( x, ] Ω ( N dω= 0 Partial Integration leads to the Weak Formulation ( α = 0 ): k N j N idω+ v N jnidω uj = f NidΩ, i = 1,..., m Ω j= 1 Ω Ω i A u = b Linear System of Equations

7 Diffpack Implementation - inheritance C++ Classes SimCase FEM FEM ConvDiff Inheritance Inheritance Fundamental library class for any simulation Fundamental library class for finite element methods General implementation of the problem. Focus on numerics

8 Diffpack Implementation - important member global_menu.multipleloop (S) FEM::makeSystem S::adm S::define S::scan FEM::calcElmMatVec FEM::numItgOverElm S::solveProblem S::integrands S::resultReport

9 Main Program GUI is added automatically Initialize Diffpack Engine Define Simulator Object Go!!!

10 class ConvDiff FEM FEM Data Structures ConvDiff ConvDiff Numerical Heart User Interaction: Menu, Gui, Pre- and Post Assemble and solve Au=b

11 ConvDiff:: integrands (numerical Heart) m k N N dω+ j i j= 1 Ω Ω Au α=0 v N jnidω u Weak Formulation ( ): j = = Ω f N dω, i = 1,..., m i b

12 ConvDiff :: fillessbc (apply essential boundary Conditions) Apply Boundary Conditions: u ( x, = 0, x, y Γ 1 essential conditions

13 ConvDiff :: solveproblem (assemble and solve Au=b)

14 ConvDiff :: define (Menu system) Main Menu System Linear Solver Submenu Int. Rules Submenu Results handling

15 Running the Application ConvDiff

16 Run-Time Control Menu structure (Input) Menu structure (GUI)

17 Diffpack - Starting a job Generate mesh (makegrid) Start application Menu: assign mesh (file), adjust options Convert results, e.g. vtk Display results Windows: GUI-application ParaView (vtk-format) Automation using input file ConvDiff SwirlFlow

18 Diffpack Job: Mesh Generate mesh example SteadyHeating\mesh\ makegrid < box.i Generats a unit square mesh Darstellung (Unix/Linux, Windows mit cygwin) plotmtvgrid box Windows: GUI-Applikation Grid Control Tools -> Grid Generation

19 Meshing Tools Datafilter import Superelement: Geometry is defined as an assembly of several elements, each element will be meshed for itself Build-in grid generators for simple test geometries interface to Geompack Triangle

20 Diffpack Job: start application > app Menu: h - help set... - change value sub... - enter submenu ok - leave menu / submenu Input file to simplify start job app -D test.i

21 Diffpack Job: Postprocessing Convert results into vtk-format Windows: start GUI application Load Datasets

22 Postprocessing by Paraview Paraview