Asphericalharmonics—Finiteelementdiscretizationoftheself-adjointangularfluxneutrontransportequationOriginalResearchArticle

Thesphericalharmonics(PN)methodiswidelyusedinsolvingtheneutrontransportequation,butithassomedisadvantages.OneofthemcomesfromthecomplexityofthePNequations.Anotheronecomesfromthedifficultyofdealingwiththevacuumboundaryconditionexactly.Inthispaper,thePNmethodisappliedtotheself-adjointangularflux(SAAF)neutrontransportequationandasetofPNmomentsequationscoupledwitheachotherareobtained.Aniterativemethodisutilizedtodecouplethemandsolvethemmomentbymoment.ThecorrespondingvacuumboundaryconditionisderivedbasedontheMarshakboundarycondition.Thespatialvariablesarediscretizedonunstructured-meshesbyuseofthefiniteelementmethod(FEM).Thenumericalresultsofseveralproblemsdemonstratethatthismethodcanprovidehighprecisionresultsandavoidtherayeffect,whichappearsinthediscreteordinate(SN)method,withrelativelyhighcomputationalefficiency.