## Computational Multiscale Modeling of Fluids and Solids: Theory and ApplicationsThe idea of the book is to provide a comprehensive overview of computational physics methods and techniques, that are used for materials modeling on different length and time scales. Each chapter first provides an overview of the basic physical principles which are the basis for the numerical and mathematical modeling on the respective length-scale. The book includes the micro-scale, the meso-scale and the macro-scale, and the chapters follow this classification. The book explains in detail many tricks of the trade of some of the most important methods and techniques that are used to simulate materials on the perspective levels of spatial and temporal resolution. Case studies are included to further illustrate some methods or theoretical considerations. Example applications for all techniques are provided, some of which are from the author’s own contributions to some of the research areas. The second edition has been expanded by new sections in computational models on meso/macroscopic scales for ocean and atmosphere dynamics. Numerous applications in environmental physics and geophysics had been added. |

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### Contents

1 | |

2 | |

3 | |

2 Multiscale Computational Materials Science | 29 |

3 Mathematical and Physical Prerequisites | 109 |

4 Fundamentals of Numerical Simulation | 175 |

Part II Computational Methods on Multiscales | 213 |

5 Computational Methods on ElectronicAtomistic Scale | 215 |

8 Perspectives in Multiscale Materials Modeling | 361 |

A Further Reading | 365 |

B Mathematical Definitions | 367 |

C Sample Code for the Main Routine of a MD Simulation | 369 |

D A Sample Makefile | 371 |

E Tables of Physical Constants | 374 |

383 | |

402 | |

6 Computational Methods on AtomisticMicroscopic Scale | 257 |

7 Computational Methods on MesoscopicMacroscopic Scale | 313 |

### Other editions - View all

Computational Multiscale Modeling of Fluids and Solids: Theory and Applications Martin Steinhauser No preview available - 2016 |

Computational Multiscale Modeling of Fluids and Solids: Theory and Applications Martin Steinhauser No preview available - 2009 |

### Common terms and phrases

algorithm applications approximation atoms axioms basic basis behavior calculated called Chap classical components concept configuration considered continuum coordinate system covariant curve defined definition denoted density derivative differential equations discussed distance Einstein electron equations of motion equilibrium Euclidean example field theory finite element fluid force formulation fundamental Hamiltonian Hartree–Fock Hence initial integral interaction introduced length scales linear vector space macroscopic manifold mass materials science mathematical matrix MD simulation methods metric metric space Minkowski Minkowski space molecular dynamics molecules Newton’s notation obtains one-forms open sets pair parameters particles phase space physical theories polymer potential principle problem properties quantum mechanics quantum theory real numbers recursive scalar Schrödinger equation Sect solid solution solving spacetime structure subset symmetry tensor term theorem thermodynamics topological space topology total energy transformation Turing machine usually variables vector space velocity wave function