## Accurate Boundary Treatment in Shallow Water Flow Computations |

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### Contents

INTRODUCTION | 1 |

MATHEMATICAL DEFINITIONS AND TOOLS | 23 |

REVIEW OF EXISTING METHODS | 43 |

4 other sections not shown

### Common terms and phrases

ADI-splitting advection amplitude analytical applied approximation assumed behaviour bottom friction boundary point boundary relations boundary treatment central differences characteristic formulation closed boundary considered corner point denotes determined difference equations differential equations discretization Duhamel's principle eigenvalues Engquist Experiment extra field equations finite difference finite difference method finite element method flow field fourier Gaussian elimination grid half time step higher order hyperbolic problem implicit inflow initial integration Kreiss linear low reflection boundary Majda matrix nonlinear numerical open boundaries order low reflection order terms outflow outflow boundary partial differential equations perturbation pseudo-differential operator reflection boundary conditions reflection principle scheme second order accuracy shallow water equations shallow water flow smoothing solution of eq solved stability streamline symbol technique theorem tion truncation error two-dimensional values vanish variables vector velocity virtual points wave solution well-posed well-posedness wordt yields zero