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A Student’s Guide to the Navier–Stokes Equations by JUSTIN W. GARVIN is a book available to read on EtoBox.

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Cover 1 Half-title page 3 Series page 4 Title page 5 Copyright page 6 About this book 7 Contents 9 Preface 11 Acknowledgments 13 1 Mass Conservation and the Continuity Equation 15 1.1 Conservation in Fluid Mechanics 15 1.2 Conservation of Mass in One Dimension 18 1.3 The Continuity Equation 22 1.4 Discussion of the Continuity Equation 30 1.4.1 The Divergence Theorem 32 1.4.2 The Unknowns in the Continuity Equation 36 1.4.3 The Concept of Steady State 37 1.4.4 Incompressible Flow 41 Problems 44 2 The Material Derivative: The First Step to the Navier–Stokes Equations 46 2.1 Lagrangrian and Eulerian Descriptions 47 2.2 The Advection and Inviscid Burgers’ Equation 54 2.2.1 Advection Equation 54 2.2.2 Inviscid Burgers’ Equation 60 2.3 The Material Derivative and the Continuity Equation 65 2.4 The Material Derivative in the Navier–Stokes Equations 69 2.5 Take Home Points 71 Problems 72 3 Force Balance, the Stress Tensor, and the Navier–Stokes Equations 74 3.1 Forces on a Fluid and the Stress Tensor 74 3.1.1 Angular Momentum and Stress Tensor Symmetry 81 3.1.2 Total Force Expression 83 3.2 General Force Balance: Cauchy’s First Law of Motion 83 3.2.1 Divergence of the Stress Tensor 84 3.3

Author

JUSTIN W. GARVIN

Language

EN