6-通量差分

16.6.1GodunovGodunov()tx??+=fww0GodunovRiemannGodunovRiemannGodunov2Godunovntt=(),nxtw%jx1122,jjxx-+(),nxtw%njw(),nxtw%(),nnjjxt=ww%(),nxtw%3()12121,jjxnnjxtdx+-=Dww%()()()()2221,,2nnjjjjjtxtxxxx=+?+?+??()()()()()1212112211222222211,21,12jjjjjjxnnjjjjxjjxxnjjxxjjxtxxdxxxxtdxdxxx+-++--=+?+?+D???????=?????D???????+?????()12122jjxjxxd+-???-+y???tLjyx=-()()11122211122222223211,2111,2120xxxnnjjxxxjjnjjjxtdyydyydyxxxxtxxxxxDDD-D-D-D?????=???????D?????????=+?+????D????()()2,njxtx???y=+Dw%4(),nxtw%(),njxtw%1jx+1322,jjxx++(),nxtw%1nj+w1,jjxx+Riemann()()()12121111,,,,,,nnjjnnjjjnnjjjxxxttttxxtxxxxtxxx++++++?????+=???????=????????=??????fww0(),xtw%1ntt+=()1,nxt+w%Godunov56.20uuatx+=aaaa+-=+02aaa++=02aaa--=1110nnnnnnjjjjjjuuuuuuaatxx+-++----++=DDD()()()()1111122nnnnnnnnnnjjjjjjjjjjuuuuuuuuuuaatxx++-+--+-----+=DDD()tx??+=fww066.3Roe()tx??+=fww0tx+=wwA011nnnnjjjjtx+---+=DDwwff011nnnnjjjjtx+---+=DD(),LR=wwAA%%()RLRL-=-ffAww%1Lj=-Rj=A%AAdd=fAwRoeA%UA%1%2%m%7A%R%121m-???????=????????RAR%%%%%O%()RLRL-=-ffAww%LR==(),=AAww%()()()()112211221111122nnnnnnnnjjjjjjjjnnnnnnjjjjjjtxx++-+-+-+--+--+DD---=DAwwA()121,nnnjjj++=AAww%%()121,nnnjjj--=AAww%%8U()()()()1122111111nnnnnnnnnnnnjjjjjjjjjjjj+-+-+-+--+-=-+-=-AwwAwwffffff%%()()11221111122nnnnnnnnnnjjjjjjjjjjtxx++-+-+------+=DDDAwwA=ARDR%%%%12m?????????=??????????D%%%O%()()1122111122nnnnnnjjjjjj++++=+--fffAww%9()()1122111122nnnnnnjjjjjj----=+--fffAww%()11221nnnnjjjjtx+++D=--Dwwff12nj+f()()()11221121nnnmjjjj-+++=-Rww%@L()()()()1111222211121212nnnnnjjjjjjmmm-+++++-==DRwwD%%%%%%L@L1r%2r%Lmr%12nj+R%()()()111112222211211122nnnnnnnmjjjjjjjmm-++++++=-==+++ARDRwwRrrr%%%%%L%%%L12nj-fRoeUA%uh10?LLRRLRuuu??=+?LLRRLRhhh??=+221112hcu=+-?c()21??12hu?=--??RoeRoeA%Roe()222220103312211322112uuuuccuugggggggg?????????????????????????????-=------++--A211112ucuuchucuhuc????????????????=-+-+R11()()()()12222222222221112222111121112222uucuccccuucccuucuccccggggggggg-??????????????????????????????-+------=-------+-Ruch(,?u=AA%)?c(?u=RR%,,?c?h??(11?u--=RR%,,?c?h??A%1?u=-%?c2?u=%3?u=+%?cRoeA%UA%AUA%LRuuu==LRhhh==?uu=?hh=?cc=UA(),uc=AA2LRuuu+=2LRhhh+=(),LLLuc=AA(),RRRuc=AA122LR+=AAAU6.4MUSCLRoeMUSCLLwRw12nj+f12j-+wnjw12j++w1nj+w12nj-f12j--w1nj-w12j+-wnjw()()()1111112222221122nnjjjjjj-++-++++++=+--ffwfwAww%()()()1111112222221122nnjjjjjj-++-------=+--ffwfwAww%13MUSCL()111222,njjj-++++=AAww%%()111222,njjj-+---=AAww%%6.5A%%0x=()222xxQxxx??3???=??+????140x=,-x=?D%()()()12mQQQ?????????=??????????D%%%O%()lllQ=%1,2,,lm=L