Introductory Finite Volume Methods for PDEs

Professor D. M. Causon, Professor C. G. Mingham and Dr. L. Qian Introductory Finite Volume Methods for PDEs Download free ebooks at bookboon.com 2 Introductory Finite Volume Methods for PDEs © 2011 Professor D. M. Causon, Professor C. G. Mingham and Dr. L. Qian & Ventus Publishing ApS ISBN 978-87-7681-882-1 Download free ebooks at bookboon.com 3 Introductory Finite Volume Methods for PDEs Contents Contents Preface 7 1 Introduction 8 1.1 Introduction 8 1.2 Obtaining the Integral Form from the Differential Form 8 1.3 Finite Volume Meshes 10 1.4 Discretising the Semi-Integral Equation 11 1.5 Implementation 14 2 Finite Volume Schemes 18 2.1 Introduction 18 2.2 FVM on a Cartesian Mesh 19 2.3 Finite Volume Schemes in 1D and 3D 22 2.4 Time Step Calculation for a Finite Volume Scheme 25 2.5 Finite Volume FOU 2D Scheme 26 2.6 Boundary Conditions 27 2.7 Coding a Finite Volume Solver 29 The next step for top-performing graduates Masters in Management Designed for high-achieving graduates across all disciplines, London Business School’s Masters in Management provides specific and tangible foundations for a successful career in business. This 12-month, full-time programme is a business qualification with impact. In 2010, our MiM employment rate was 95% within 3 months of graduation*; the majority of graduates choosing to work in consulting or financial services. As well as a renowned qualification from a world-class business school, you also gain access to the School’s network of more than 34,000 global alumni – a community that offers support and opportunities throughout your career. For more information visit www.london.edu/mm, email mim@london.edu or give us a call on +44 (0)20 7000 7573. * Figures taken from London Business School’s Masters in Management 2010 employment report Download free ebooks at bookboon.com 4 Introductory Finite Volume Methods for PDEs Contents 3 Derivation of Equations 33 3.1 Introduction 33 3.2 Conservation Laws 33 3.3 Control Volume Approach 33 3.4 Deriving the Integral Form of the 2D Linear Advection Equation 35 3.5 Deriving the Differential Form of the 2D Linear Advection Equation 36 4 Further Finite Volume Schemes 39 4.1 Introduction 39 4.2 Linear Interpolation 39 4.3 Quadratic Interpolation 42 4.4 Converting from Finite Difference to Finite Volume 43 5 Systems of Equations 48 5.1 Introduction 48 5.2 The Shallow Water Equations 48 5.3 General FVS for the SWE 50 5.4 FVS for the 2D SWE on a Structured Mesh 51 5.5 Heuristic Time Step for a 2D SWE FVS 53 Teach with the Best. Learn with the Best. Agilent offers a wide variety of affordable, industry-leading electronic test equipment as well as knowledge-rich, on-line resources —for professors and students. We have 100’s of comprehensive web-based teaching tools, lab experiments, application notes, brochures, DVDs/ CDs, posters, and more. © Agilent Technologies, Inc. 2012 See what Agilent can do for you. www.agilent.com/find/EDUstudents www.agilent.com/find/EDUeducators u.s. 1-800-829-4444 canada: 1-877-894-4414 Download free ebooks at bookboon.com 5 ... - tailieumienphi.vn