Riemann solvers and numerical methods for fluid dynamics. A practical introduction. 2nd ed.

*(English)*Zbl 0923.76004
Berlin: Springer. xix, 624 p. (1999).

[See the review of the first edition (1997; Zbl 0888.76001).]

This second edition includes a number of minor changes. First, we have corrected all the errors found. Having used the book for lectures, since the publication of the first edition in 1997, has been useful in re-assessing some of the material and its mode of presentation. We have added new references in appropriate sections, in an attempt to partially correct the unavoidable injustice of excluding reference to many valuable contributions to the themes of interest of this book. We have also added a new test problem to the existing suite of tests. The new test problem has the purpose of illustrating via practical numerical results the main differences between upwind and centred methods and between Godunov and most flux vector splitting methods. Finally, we also admit to having re-plotted all the numerical results of the first edition that had a position error of \(\Delta x\).

This second edition includes a number of minor changes. First, we have corrected all the errors found. Having used the book for lectures, since the publication of the first edition in 1997, has been useful in re-assessing some of the material and its mode of presentation. We have added new references in appropriate sections, in an attempt to partially correct the unavoidable injustice of excluding reference to many valuable contributions to the themes of interest of this book. We have also added a new test problem to the existing suite of tests. The new test problem has the purpose of illustrating via practical numerical results the main differences between upwind and centred methods and between Godunov and most flux vector splitting methods. Finally, we also admit to having re-plotted all the numerical results of the first edition that had a position error of \(\Delta x\).

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76M20 | Finite difference methods applied to problems in fluid mechanics |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |