双曲问题用的有限体积方法（英文版）

Thisbookcontainsanintroductiontohyperbolicpartialdifferentialequationsandapowerfulclassofnumericalmethodsforapproximatingtheirsolution,includingbothlinearproblemsandnonlinearconservationlaws.Theseequationsdescribeawiderangeofwavepropagationandtransportphenomenaarisinginnearlyeveryscientificandengineeringdiscipline.Severalapplicationsaredescribedinaself-containedmanner,alongwithmuchofthemathematicaltheoryofhyperbolicproblems.High-resolutionversionsofGodunov'smethodaredeveloped,inwhichRiemannproblemsaresolvedtodeterminethelocalwavestructureandlimitersarethenappliedtoeliminatenumericaloscillations.Thesemethodswereoriginallydesignedtocaptureshockwavesaccurately,butarealsousefultoolsforstudyinglinearwave-propagationproblems,particularlyinheterogenousmaterial.ThemethodsstudiedareimplementedintheCLAWPACKsoftwarepackage.Sourcecodeforalltheexamplespresentedcanbefoundontheweb,alongwithanimationsofmanytimedependentsolutions.Thisprovidesanexcellentlearningenvironmentforunderstandingwave-propagationphenomenaandfinitevolumemethods.