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1、Thevis
ousgasringasanastrophysi
altestproblemforavis
ousSH-
odeR.SpeithandH.Ri ertnstitutfurAstronomieundAstrophysik,UniversitatTubingen,D-72076Tubingen,GermanyAbstra
tWepresentthegeneralanalyti
solutionofavis
ousgasringarounda
entralmass.Thissolutionisusedtotestafurtherdevelopmentofthesmoo
2、thedparti
lehydro-dynami
s(SH)algorithm,whi
his
apableofsimulatingproblemswithphysi
alvis
osity(here:withkinemati
vis
osity).Wedis
usssomeSHsimulationresultsand
on
ludesomefundamentalpropertiesofthealgorithm.eywords:umeri
alHydrodynami
s,arti
leethods,SHBen
hmarkroblem1ntrodu
tionAla
3、rge
lassofproblemsintheoreti
alastrophysi
sisrelatedtothedynami
sof
ompressible
owsin
ludingmanyphysi
ale e
tssu
hasgravity,radiation,vis
osity,ele
tri
hargesand
urrents,ormagneti
elds.Theseproblemsareatta
kedprimarilythroughnumeri
alsimulations,anddi erentnumeri
almethodsforvariousaspe
tsof
4、astrophysi
algasdynami
shavebeendevelopedinthepastorare
urrentlyinthestateofdevelopment.Thesealgorithmshavetobetestedinordertoverifytheirstability,a
ura
y,androbustness.Anidealtestis,of
ourse,a
omparisonwithamodelproblemwhereananalyti
solutionisknown,andexamplesforone-dimensional
owsin
ludet
5、hewell-knownshoktube,adve
tionproblems(seethearti
leof.Stone[14℄inthisvolume),orself-similarsolutionsoftheEulerequationforaperfe
tgas.Formanynumeri
almethodserrorestimatesareimpossibletoobtain,andanalyti
solutions
anbeusedtodetermineerrorboundsempiri
ally.Thisisevenmoreimportantwhenthemathem
6、ati
alfoundationsofthemethodarepoorlyunderstood,andonesu
hmethodisSmoothedarti
leHydrodynami
s(SH).Fortwo-orthree-dimensionalgas
owsanalyti
allysolvableproblemsarerarebutthereisoneastrophysi
allyinterestingexamplewhereatleastreprintsubmittedtoElsevierreprint25uly1999anapproximatesolution
7、ofthehydrodynami
equations
anbefound.Thisis
on
ernedwithathingasdiskthatmovesarounda
entralpointmassunderthein
uen
eofgravityandvis
oustorques.frotationalsymmetryisassumedanevolutionequationforthedensity
anbederived,andfora
onstantkinemati
v
