Domain Decomposition Techniques for Boundary Elements : Application to Fluid Flow (Advances in Boundary Elements)

Covers subdomain techniques of the Boundary Element Method. The book will be useful to all scientists and engineers interested in waves and lfuids, including graduate students, postdoctoral researchers, and academics, marine, civil and mechanical engineers, meteorologists and oceanographers. WIT Press Cover 1 Domain Decomposition Techniques for Boundary Elements: Application to Fluid Flow 2 Copyright Page 7 Contents 8 Preface 14 Chapter 1: Diffusion–convection problems 18 1. Introduction 18 2. Boundary element formulations 20 3. Numerical implementation 25 4. Numerical stability for homogeneous diffusion–convection 29 5. Numerical examples of diffusion–convection problems 33 6. Burgers' equation 37 7. Numerical formulations of Burgers' equation 38 8. Numerical examples of Burgers' equation 42 9. Conclusion 46 Chapter 2: Viscous compressible fluid dynamics 50 1. Introduction 50 2. Conservation equations 51 3. Linear gradient type of constitutive models 52 4. Primitive variables formulation 53 5. Velocity–vorticity formulation 55 6. Pressure equation 58 7. Boundary-domain integral equations 59 8. Discrete models 72 9. Test example: differentially-heated tall enclosure 75 10. Conclusions 83 Chapter 3: Multi-domain DRM boundary element method for the numerical simulation of non-isothermal Newtonian and non-Newtonian flow problems 86 1. Introduction 86 2. Thermal convection Newtonian flow problems 89 3. Non-isothermal non-Newtonian Stokes flow with viscous dissipation 101 4. Conclusion 113 Chapter 4: Modelling flow and solute transport in fractured porous media using the DRM multidomain technique 116 1. Introduction 116 2. Governing equations 120 3. Numerical method 126 4. Numerical implementation 133 5. Coupling strategy 145 6. Numerical results 149 7. Conclusion 160 Chapter 5: Parallel domain decomposition boundary element method approach for large-scale transient and steady nonlinear heat conduction 164 1. Introduction 164 2. Explicit domain decomposition 166 3. Iterative solution algorithm 168 4. Parallel implementation on a PC cluster 171 5. Applications in heat transfer 174 6. Numerical validation and examples 182 7. Conclusions 199 Chapter 6: Computational implementation for 3D problems 204 1. Introduction 205 2. Equations and DRM formulation 206 3. The dual reciprocity method multidomain approach 209 4. Schematic view of a DRM code for Poisson's problems 212 5. General aspects of DRM-MD implementation for Poisson’s problems 213 6. A 3D DRM-MD implementation for Poisson's problems using discontinuous elements 215 7. A 3D DRM-MD implementation for Poisson's problems using continuous elements 221 8. A 3D DRM-MD implementation for advection–diffusion problems 223 9. A convenient arrangement 225 10. Examples 227 11. Transient advection–diffusion 244 12. Conclusions 250 Chapter 7: Iterative schemes for the solution of systems of equations arising from the DRM in multidomains 254 1. Introduction 254 2. Preliminary remarks on the BEM 257 3. The dual reciprocity approximation 259 4. Approximating functions fj 267 5. Iterative solution methods for sparse linear systems 269 6. Numerical analysis 282 7. Conclusions 310 ISBN-10,/,ASIN:,1845641000,ISBN-13,/,EAN:,9781845641009 ISBN-10 / ASIN:,1845641000,ISBN-13 / EAN:,9781845641009 The sub-domain techniques in the BEM are nowadays finding its place in the toolbox of numerical modellers, especially when dealing with complex 3D problems. We see their main application in conjunction with the classical BEM approach, which is based on a single domain, when part of the domain needs to be solved using a single domain approach, the classical BEM, and part needs to be solved using a domain approach, BEM subdomain technique. This has usually been done in the past by coupling the BEM with the FEM, however, it is much more efficient to use a combination of the BEM and a BEM sub-domain technique. The advantage arises from the simplicity of coupling the single domain and multi-domain solutions, and from the fact that only one formulation needs to be developed, rather than two separate formulations based on different techniques. There are still possibilities for improving the BEM sub-domain techniques. However, considering the increased interest and research in this approach we believe that BEM sub-domain techniques will become a logical choice in the future substituting the FEM whenever an efficient solution requires coupling of the BEM with a domain technique.