Contents
xvii
8 Nonreflecting Boundary Conditions
395
8.1 One-Dimensional Flow. . . . . . . . . . . . . . . .
397
8.1.1 Well-Posed Initial-Boundary Value Problems.
397
8.1.2 The Radiation Condition . . . . . . . .
400
8.1.3 Time-Dependent Boundary Data . . . .
401
8.1.4 Reflections at an Artificial BoundaryThe Continuous Case . . . . . . . . . .
402
8.1.5 Reflections at an Artificial BoundaryThe Discretized Case
403
8.1.6 Stability in the Presence of Boundaries .
409
8.2 Two-Dimensional Shallow-Water Flow
8.2.1 One-Way Wave Equations .
412
414
8.2.2 NumericalImplementation ..
419
8.3 Two-Dimensional Stratified Flow . .
419
8.3.1 Lateral Boundary Conditions .
420
8.3.2 Upper Boundary Conditions .
424
8.3.3 Numerical Implementation of the Radiation Upper
Boundary Condition
429
8.4 Wave-Absorbing Layers
431
8.5 Summary .
436
Problems . . . . . . . . . . .
437
Appendix Numerical Miscellany
439
A.1 Finite-Difference Operator Notation
439
A.2 Tridiagonal Solvers
440
A.2.1 Code for a Tridiagonal Solver
440
A.2.2 Code for a Periodic Tridiagonal Solver .
441
Bibliography
443
Index
457