简介:Thispaperpresentsasimpleapproachforimprovingtheperformanceoftheweightedessentiallynonoscillatory(WENO)finitevolumeschemeonnon-uniformgrids.ThistechniquereliesonthereformulationofthefifthorderWENO-JS(WENOschemepresentedbyJiangandShuinJ.Comput.Phys.126:202–228,1995)schemedesignedonuniformgridsintermsofonecell-averagedvalueanditsleftand/orrightinterfacialvaluesofthedependentvariable.Theeffectofgridnon-uniformityistakenintoconsiderationbyaproperinterpolationoftheinterfacialvalues.Onnonuniformgrids,theproposedschemeismuchmoreaccuratethantheoriginalWENO-JSscheme,whichwasdesignedforuniformgrids.Whenthegridisuniform,theresultingschemereducestotheoriginalWENO-JSscheme.Inthemeantime,theproposedschemeiscomputationallymuchmoreefficientthanthefifth-orderWENOschemedesignedspecificallyforthenon-uniformgrids.Anumberofnumericaltestcasesaresimulatedtoverifytheperformanceofthepresentscheme.
简介:快打扫方法的高顺序最近在文学被开发了高效地解决静态的Hamilton-Jacobi方程。与快打扫方法的第一份订单作比较,快大规模的高顺序方法是更精确的,但是因为精确地在流入边界附近对待点是特别地重要的更宽的数字模板,他们经常在边界附近为几个格子点要求另外的数字边界处理,当信息将流进计算领域并且将影响全球精确性。在文学,在这些边界点的数字答案也与准确答案被修理,它不总是是可行的,或与第一顺序discretization计算了,它能减少全球精确性。在这篇论文,我们讨论二策略处理流入边界条件。一个人基于快在边界和理查森推测附近与几种不同网孔尺寸打扫方法的第一份订单的数字答案,其它基于一个Lax-Wendroff类型过程到反复利用PDE以正切的衍生物给正常写空间衍生物到流入边界,从而在格子获得高顺序解决方案值指在流入边界附近。我们用快大规模高度探索这二条途径顺序WENO计划在[18]为作为一个代表性的例子解决静态的Eikonal方程。数字例子被给表明这二条途径的表演。
简介:Astrictproofofthehyperbolicityofthemulti-classLWR(Lighthill-Whitham-Richards)trafficflowmodel,aswellasthedescriptionsonthosenonlinearwavescharacterizedinthetrafficflowproblemsweregiven.Theyweremainlyaboutthemonotonicityofdensitiesacrossshocksandinrarefactions.Asthesystemhadnocharacteristicdecompositionexplicitly,ahighresolutionandhigherorderaccuracyWENO(weightedessentiallynon-oscillatory)schemewasintroducedtothenumericalsimulation,whichcoincideswiththeanalyticaldescription.