The shallow water equations in geomorphic modeling

Slides:

Advertisements

Similar presentations

SolidWorks Flow Simulation

Advertisements

Modelling tools - MIKE11 Part1-Introduction

Institute of Energy and Sustainable Development Improvement of a Two-Dimensional (2D) Borehole Heat Exchanger (BHE) Model Miaomiao He, Simon Rees, Li Shao.

Development and Implementation of Depth Dependent Wave Forcing and Stokes Drift into Coupled 3D PADCIRC/PUNSWAN Joshua Todd Coastal Engineering Department.

EROS (Crave & Davy, 2001) “Stochastic model of erosion– sedimentation processes, based on cellular automata, which mimics the natural variability of climatic.

Fluidyn FLOWCOAST FLOOIL 3D Fluid Dynamics Model to Simulate Oil slick movement in coastal waters or rivers FLOOIL.

UNIVERSITY OF SOUTH CAROLINA Erosion rate formulation and modeling of turbidity current Ao Yi and Jasim Imran Department of Civil and Environmental Engineering.

Dynamics I 23. Nov.: circulation, thermal wind, vorticity 30. Nov.: shallow water theory, waves 7. December: numerics: diffusion-advection 14. December:

Sediment Movement after Dam Removal

Ground-Water Flow and Solute Transport for the PHAST Simulator Ken Kipp and David Parkhurst.

A.Erosion – The transportation of weathered sediments 1. Agents of Erosion or Transport Systems: a. Running water b. Wind c. Glaciers d. Waves & Tidal.

Accurate Numerical Treatment of the Source Terms in the Non-linear Shallow Water Equations J.G. Zhou, C.G. Mingham, D.M. Causon and D.M. Ingram Centre.

1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, CHAPTER 13: THE QUASI-STEADY APPROXIMATION.

Use of satellite altimeter data for validating large scale hydraulic models Matt Wilson, University of Exeter Doug Alsdorf, Ohio State University Paul.

STORM SURGE. Composed of several attributes: A)Barometric – Coastal water response to low pressure at center of storm B) Wind stress – frictional drag.

Computational Investigations of Gravity and Turbidity Currents Eckart Meiburg UC Santa Barbara Motivation Governing equations / computational approach.

Modeling Fluid Phenomena -Vinay Bondhugula (25 th & 27 th April 2006)

Physics of fusion power Lecture 2: Lawson criterion / some plasma physics.

A TWO-FLUID NUMERICAL MODEL OF THE LIMPET OWC CG Mingham, L Qian, DM Causon and DM Ingram Centre for Mathematical Modelling and Flow Analysis Manchester.

Juan Carlos Ortiz Royero Ph.D.

HYDRAULICS AND SEDIMENT TRANSPORT: RIVERS AND TURBIDITY CURRENTS

St Venant Equations Reading: Sections 9.1 – 9.2.

Physics of Fusion power Lecture4 : Quasi-neutrality Force on the plasma.

Fixed and Fluidized Beds

A Circulation Model to Investigate the Movement of Wastes from an Open Ocean Aquaculture Site David W. Fredriksson U. S. Naval Academy NOAA Research -

Hydraulic Routing in Rivers

Dynamic Characteristics of Break Debris Flow and its Numerical Simulation State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Chengdu.

Diogo Bolster 120 c Cushing Hall

Fritz R. Fiedler University of Idaho Department of Civil Engineering Simulation of Shallow Discontinuous Flow over Complex Infiltrating Terrain.

Modelling Hydrodynamical Processes of the Pacific Ocean Littoral and the Amur River (the Far Eastern Region of Russia) K. A. Chekhonin Resheach Institute.

Solution of the St Venant Equations / Shallow-Water equations of open channel flow Dr Andrew Sleigh School of Civil Engineering University of Leeds, UK.

Nicole Gasparini Arizona State University Landscape Modeling.

Landscape Evolution Modeling ERODE Irina Overeem, February 2013.

A conservative FE-discretisation of the Navier-Stokes equation JASS 2005, St. Petersburg Thomas Satzger.

Numerical Investigation into Potential Flow Around High-speed Hydrofoil Assisted Craft ZHONGYU YANG supervised by Prof G.E HEARN and.

1 Numerical simulation software LinkFEA Iris Summer Academy 2011 Mengxi WU Institue of Mechanics,CAS 04\09\2011 (WP4)

The Governing Equations The hydrodynamic model adopted here is the one based on the hydrostatic pressure approximation and the boussinesq approximation,

Distributed Flow Routing Surface Water Hydrology, Spring 2005 Reading: 9.1, 9.2, 10.1, 10.2 Venkatesh Merwade, Center for Research in Water Resources.

Geometry Group Summer 08 Series Toon Lenaerts, Bart Adams, and Philip Dutre Presented by Michael Su May

Physical Oceanography SACS/AAPT Spring Meeting March 29, 2003 Coastal Carolina University.

Gesa-Partner 8 East-Macedonia Thrace – Participants: Prof N Kotsovinos, Prof. C Koutitas,, Prof. V Hrissanthou, and the M.Sci. Eng. A. Georgoulas,A Samaras,

Mathematical Background

Lecture Objectives Unsteady State Simulation Example Modeling of PM.

MIKE 11 IntroductionNovember 2002Part 1 Introduction to MIKE 11 Part 1 General Hydrodynamics within MIKE 11 –Basic Equations –Flow Types Numerical Scheme.

The Littoral Sedimentation and Optics Model (LSOM)

© Fluent Inc. 11/24/2015J1 Fluids Review TRN Overview of CFD Solution Methodologies.

Hydraulic Routing in Rivers Reference: HEC-RAS Hydraulic Reference Manual, Version 4.1, Chapters 1 and 2 Reading: HEC-RAS Manual pp. 2-1 to 2-12 Applied.

HEAT TRANSFER FINITE ELEMENT FORMULATION

Xiaoming Wang and Philip L.-F. Liu Cornell University

Two Dimensional simulation of a Dam Break wave propagation for the isolated building test case University of Pavia Gabriella Petaccia Impact Workshop...

Ekman pumping Integrating the continuity equation through the layer:. Assume and let, we have is transport into or out of the bottom of the Ekman layer.

On the Use of Finite Difference Matrix-Vector Products in Newton-Krylov Solvers for Implicit Climate Dynamics with Spectral Elements ImpactObjectives 

A Non-iterative Hyperbolic, First-order Conservation Law Approach to Divergence-free Solutions to Maxwell’s Equations Richard J. Thompson 1 and Trevor.

1 INTRODUCTION TO “Stratigrafia” The code in the workbook “stratigrafia” computes - longitudinal profiles; - water surface elevation; - sediment transport.

Evaluation of Erosion- Sedimentation processes in River Basins Valeriy Klenov Valeriy Klenov Self Employed Russia, Moscow.

Environmental Hydrodynamics Lab. Yonsei University, KOREA RCEM D finite element modeling of bed elevation change in a curved channel S.-U. Choi,

A Fully Conservative 2D Model over Evolving Geometries Ricardo Canelas Master degree student IST Teton Dam 1976.

Weakly nonlinear analysis of dunes by the use of a sediment transport formula incorporating the pressure gradient Satomi Yamaguchi (Port and airport Institute,

An introduction to cohesive sediment transport modelling

Modelling of Marine Systems. Shallow waters Equations.

EXAMPLE Water flows uniformly in a 2m wide rectangular channel at a depth of 45cm. The channel slope is and n= Find the flow rate in cumecs.

Transient Mixed Flow Modeling Capability in SRH-2D for Culverts and Bridges Yong G. Lai.

Fluid Structure Interactions Research Group

A TWO-FLUID NUMERICAL MODEL OF THE LIMPET OWC

Lecture Objectives Unsteady State Ventilation Modeling of PM.

Distributed Flow Routing

Modelling tools - MIKE11 Part1-Introduction

Diffusion Through Porous Media

Physics of fusion power

Fluvial Hydraulics CH-3

Presentation transcript:

The shallow water equations in geomorphic modeling Guy Simpson Earth Science University of Geneva - Switzerland Guy.Simpson@unige.ch

Water-induced erosion ….. in the absence of water! (drainage area - water discharge proxy) Stream-power type model (detachment-limited) Transport-limited model A (drainage area) Flux = c An Introduce poorly constrained parameters Neglect flow dynamics of water and other important physics

Model of coupled shallow water flow and erosion-sedimentation Simpson and Castelltort (2006) Computers and Geosciences

Shallow water flow over a mobile bed water mass balance x- force balance y- force balance Sediment mass balance Kinematic relationship between bed fluxes and bed elevation c sediment concentration in fluid z bed topography E entrainment flux (between bed and water) D deposition flux f porosity r density of water-sediment mixture (rw(1-c)+rsc) ro density of saturated bed (rwf+rs(1-f)) rw density of water rs density of sediment Additional forces in x direction (e.g., bed friction, bed slope)

Empirical functions for E and D (for cohesionless material) If If Shields parameter Particle Reynolds number Friction velocity

Solution obtained with finite volume method using a Riemann solver

Dam break calculation in 1-D

Dam break calculation in 2-D

Computed water surface (in meters) after 60 seconds

Velocity field of water and water depth contours after 60 seconds

Dam break over mobile bed (1-D simulation)

Water reservoir dam

Coastal sediment transport due to a Tsunami Wave : period = 30 min. amplitude = 5 m Gently sloping coast Ocean

What are the (dis/)advantages relative to alternative formulations Improved (richer) physics - wide range of applications - Flexible non-capacity sediment transport formulation Avoid ad hoc parameters Readily testable (bench-marking) Disadvantages More complicated to program (development time) Computationally more expensive (longer model run time) Numerical stability issues (paricularly for small water depths) Other issues Well developed numerical methods to solve the SWE Easy to parallelise Unstructured meshes Other numerical techniques (e.g., Lattice Boltzmann)

Vector formulation

Finite volume method

Riemann solver