Ali Sami and Clint Dawson

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Presentation transcript:

Ali Sami and Clint Dawson Hybrid Discontinuous Galerkin Methods for Serre-Green-Naghdi Water Wave Models Ali Sami and Clint Dawson Ali Samii Final doctoral exam Department of ASE/EM UT Austin

Acknowledgments

Motivation

Motivation: Long waves away from the coast

Motivation: Dispersive waves

Motivation: Dispersive waves

The Water Wave Problem: Assumptions

Shallow Water Regime

Shallow Water Regime

Shallow Water Regime

Shallow Water Regime

The Water Wave Problem: Governing equations

The Water Wave Problem: Governing equations

The Water Wave Problem: Governing equations

The Water Wave Problem: Dirichlet Neumann Operator

The Water Wave Problem: Dirichlet Neumann Operator

The Water Wave Problem: Dispersive properties

The Water Wave Problem: Dispersive properties

The Water Wave Problem: Nondimensionalization

Water Wave Problem: Asymptotic expansion

Water Wave Problem: Asymptotic expansion

Asymptotic models:

Outline

Korteweg de Vries Equation

Korteweg de Vries Equation: Solution to linear equation

Korteweg de Vries Equation: Solution procedure using HDG

Korteweg de Vries Equation: Solution procedure using HDG

Korteweg de Vries Equation: Stability of the method

Korteweg de Vries Equation: Accuracy of the results

Korteweg de Vries Equation: Nonlinear solver

Korteweg de Vries Equation: Nonlinear solver

Korteweg de Vries Equation: Nonlinear accuracy

Korteweg de Vries Equation: Nonlinear examples

Korteweg de Vries Equation: Nonlinear examples

Korteweg de Vries Equation: Nonlinear examples

Outline

NSWE: Solution approach

NSWE: Solution approach

NSWE: Solution approach

NSWE: Numerical results

NSWE: Numerical results

NSWE: Numerical results

NSWE: Numerical results

NSWE: Numerical results

Outline

Asymptotic models:

Green-Naghdi Equation: Solution approach

Green-Naghdi Equation: Strang splitting

Green-Naghdi Equation: Solving the dispersive part

Green-Naghdi Equation: Solving the dispersive part

Green-Naghdi Equation: Solving the dispersive part

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results A. Samii and C. Dawson SIAM – Computational Science and Engineering Atlanta 2017

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Green-Naghdi Equation: Numerical results

Concluding remarks

Happy Birthday Bernado!!! Thank You Happy Birthday Bernado!!!