Publisher’s description: This book addresses the problem of artificial boundaries, i.e., boundaries which have no physical counterpart. It describes the question of absorbing boundary conditions in fluid mechanics, and includes many interesting related contributions in wave propagation.
There are two situations where artificial boundaries are introduced. First, for computing in a bounded region of a problem formulated in an infinite domain and secondly, in the context of domain decomposition methods. Several methods were developed including integral equations, infinite elements, boundary layers, and fictitious boundaries with adapted boundary conditions. The latter have become very popular in geophysics and aeronautics.
Contents. Chapter 1: Introduction. Chapter 2: Historical perspective. Chapter 3: Boundary conditions for the Euler and Navier-Stokes equations: François Dubois, Partial Riemann problem, boundary conditions, and gas dynamics (16–77); F. Nicoud and T. Poinsot, Boundary conditions for compressible unsteady flows (78–108); Jan Nordström, Model problems and the analysis of boundary procedures in CFD (109–117). Chapter 4. Artificial boundary conditions for the Euler and Navier-Stokes equations: Michael B. Giles, Non-reflecting boundary conditions for Euler equation calculations (121–143); L. Tourette, Artificial boundary conditions for the linearized compressible Navier-Stokes equations (144–180); Semyon V. Tsynkov and Veer N. Vatsa, An improved treatment of external boundary conditions for three-dimensional flow computations (181–200); Thomas Hagstrom, Liyang Xu and John Goodrich, On the theory of exact and approximate boundary conditions for linearized compressible flow problems (201–216). Chapter 5. Non reflecting boundary conditions: Dan Givoli and Igor Patlashenko, Optimal local absorbing boundary conditions for problems in infinite domains (219–241); Marcus J. Grote, Nonreflecting boundary conditions (242–276). Chapter 6. Perfectly matched layer methods: Semyon Tsynkov and Eli Turkel, A Cartesian perfectly matched layer for the Helmholtz equation (279–309); Adib N. Rahmouni, The perfectly matched layers in fluid dynamics (310–338). Chapter 7. Domain decomposition methods: Bertil Gustafsson and Lina Hemmingsson-Frändén, High-order methods and domain decomposition (341–347); C. Japhet and Frédéric Nataf, The best interface conditions for domain decomposition methods: absorbing boundary conditions (348–373).