InterCell Escapade Tutorial

Diusion/Heat Equation Derive a Cellular Algorithm Running on InterCellInterCell/Escapade TutorialN. FressengeasLaboratoire Materiaux Optiques, Photonique et SystemesUnite de Recherche commune a l’Universite Paul Verlaine Metz et a SupelecDowload this document fromhttp://intercell.metz.supelec.frN. Fressengeas LMOPSInterCell/EscapadeDiusion/Heat Equation Derive a Cellular Algorithm Running on InterCellTable of contentsFick Di usion or Heat Transfer laws as an exampleFick/Heat lawsBoundary ConditionsDerive a Cellular AlgorithmInstall the necessary softwareDiscretize your problemLocate your equations on the MeshRunning on InterCellA look at the lesRun the programSee the resultsN. Fressengeas LMOPSInterCell/EscapadeDiusion/Heat Equation Derive a Cellular Algorithm Running on InterCellFick/Heat lawsSteady state Fick/Heat di usion lawsA fairly simple partial di erential problem for didactic purposeFick laws Di usion lawsI IJ = Cgrad () q = kgrad (T )@ @TI I+div (J) = 0 C +div (q) = 0@t @t@ @TI I= C4 C = k4T@t @tSteady state lawSteady state law4 = 0 4T = 0N. Fressengeas LMOPSInterCell/EscapadeDiusion/Heat Equation Derive a Cellular Algorithm Running on InterCellBoundary ConditionsSome boundary conditionsComplexity often lies in the boundary conditionsTJPure diusionqJqBoundary conditionsI Constant ow pipes : J = J = Cgrad ()0@ @I grad (J)kBoxborders : = 0 or = 0@x @yI Dirichlet : constantN. ...