The influence of normal flow boundary conditions on spurious modes in finite element solutions to the shallow water equations

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.1650181103 ◽

1994 ◽

Vol 18 (11) ◽

pp. 1021-1060 ◽

Cited By ~ 14

Author(s):

J. J. Westerink ◽

R. A. Luettich ◽

J. K. Wu ◽

R. L. Kolar

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Shallow Water ◽

Shallow Water Equations ◽

Normal Flow ◽

Flow Boundary ◽

Spurious Modes

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On normal flow boundary conditions in finite element codes for two-dimensional shallow water flow

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.1650040107 ◽

1984 ◽

Vol 4 (1) ◽

pp. 99-104 ◽

Cited By ~ 13

Author(s):

William G. Gray

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Shallow Water ◽

Water Flow ◽

Two Dimensional ◽

Normal Flow ◽

Shallow Water Flow ◽

Flow Boundary

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Transparent boundary conditions for the shallow water equations with a mixed finite element formulation

Applied Numerical Mathematics ◽

10.1016/s0168-9274(02)00140-x ◽

2003 ◽

Vol 44 (1-2) ◽

pp. 109-138 ◽

Cited By ~ 3

Author(s):

Astrid Holstad ◽

Ivar Lie

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Shallow Water ◽

Shallow Water Equations ◽

Mixed Finite Element ◽

Finite Element Formulation ◽

Element Formulation ◽

Transparent Boundary Conditions

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Energy–enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions

Journal of Computational Physics ◽

10.1016/j.jcp.2018.06.071 ◽

2018 ◽

Vol 373 ◽

pp. 171-187 ◽

Cited By ~ 7

Author(s):

W. Bauer ◽

C.J. Cotter

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Shallow Water ◽

Shallow Water Equations ◽

Slip Boundary Conditions ◽

Slip Boundary ◽

Rotating Shallow Water ◽

Finite Element Schemes ◽

Rotating Shallow Water Equations

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Finite Element Approximations to the System of Shallow Water Equations, Part III: On the Treatment of Boundary Conditions

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142998341623 ◽

2000 ◽

Vol 38 (1) ◽

pp. 149-159 ◽

Cited By ~ 2

Author(s):

Clint N. Dawson ◽

Mónica L. Martínez-Canales

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Shallow Water ◽

Shallow Water Equations ◽

Finite Element Approximations

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Normal Flow Boundary Conditions in Shallow Water Models — Influence on Mass Conservation and Accuracy

Computational Methods in Water Resources X - Water Science and Technology Library ◽

10.1007/978-94-010-9204-3_131 ◽

1994 ◽

pp. 1081-1088 ◽

Cited By ~ 1

Author(s):

R. L. Kolar ◽

W. G. Gray ◽

J. J. Westerink

Keyword(s):

Boundary Conditions ◽

Shallow Water ◽

Mass Conservation ◽

Normal Flow ◽

Flow Boundary ◽

Shallow Water Models ◽

Water Models

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Galerkin-finite element methods for the shallow water equations with characteristic boundary conditions

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw017 ◽

2016 ◽

Vol 37 (1) ◽

pp. 266-295 ◽

Cited By ~ 3

Author(s):

D. C. Antonopoulos ◽

V. A. Dougalis

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Shallow Water ◽

Finite Element Methods ◽

Shallow Water Equations ◽

Galerkin Finite Element ◽

Characteristic Boundary ◽

Galerkin Finite Element Methods

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High-Order Higdon Non-Reflecting Boundary Conditions for the Shallow Water Equations

10.21236/ada401838 ◽

2002 ◽

Cited By ~ 5

Author(s):

Dan Givoli ◽

Beny Neta

Keyword(s):

Boundary Conditions ◽

Shallow Water ◽

Shallow Water Equations ◽

High Order

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Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations of Shallow-Water Equations. Part 1: One Dimension

Journal of Scientific Computing ◽

10.1007/s10915-004-4136-6 ◽

2005 ◽

Vol 22-23 (1-3) ◽

pp. 47-82 ◽

Cited By ~ 50

Author(s):

Onno Bokhove

Keyword(s):

Finite Element ◽

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

One Dimension ◽

Galerkin Finite Element ◽

Discontinuous Galerkin Finite Element ◽

Finite Element Discretizations ◽

Flooding And Drying ◽

Element Discretizations

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Well-posed transparent boundary conditions for the shallow water equations

Applied Numerical Mathematics ◽

10.1016/s0168-9274(01)00045-9 ◽

2001 ◽

Vol 38 (4) ◽

pp. 445-474 ◽

Cited By ~ 12

Author(s):

Ivar Lie

Keyword(s):

Boundary Conditions ◽

Shallow Water ◽

Shallow Water Equations ◽

Transparent Boundary Conditions ◽

Well Posed

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RECENT DEVELOPMENTS IN THE NUMERICAL SIMULATION OF SHALLOW WATER EQUATIONS II: TEMPORAL DISCRETIZATION

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202594000303 ◽

1994 ◽

Vol 04 (04) ◽

pp. 533-556 ◽

Cited By ~ 4

Author(s):

V. AGOSHKOV ◽

E. OVCHINNIKOV ◽

A. QUARTERONI ◽

F. SALERI

Keyword(s):

Numerical Simulation ◽

Finite Element ◽

Finite Difference ◽

Shallow Water ◽

Shallow Water Equations ◽

Numerical Results ◽

Finite Difference Approximation ◽

Difference Approximation ◽

Recent Developments ◽

Numerical Approaches

This paper deals with time-advancing schemes for shallow water equations. We review some of the existing numerical approaches, propose new schemes and investigate their stability. We present numerical results obtained using the time-advancing schemes proposed, with finite element and finite difference approximation in space variables.

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