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lect_20 - Numerical Marine Hydrodynamics Partial...

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Numerical Marine Hydrodynamics Partial Differential Equations – PDE Classification – Hyperbolic PDEs – Parabolic PDEs • Heat Equation • Finite Difference Schemes – Forward Marching (Euler) – Crank-Nicholson Example – heat Equation – Elliptical PDEs • Laplace equation • Poisson equation • Helmholtz equation • Boundary conditions • Interface conditions Numerical Marine Hydrodynamics Lecture 20 2.29
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Partial Differential Equations A,B and C Constants Hyperbolic Parabolic Elliptic y φ ( n ) (x,y 2 ) Quasi-linear PDE φ ( n ) (x 1 ,y) φ ( n ) (x 2 ,y) φ ( n ) (x,y 1 ) Numerical Marine Hydrodynamics Lecture 20 2.29 x
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Partial Differential Equations Elliptic PDE Laplace Operator Examples Laplace Equation – Potential Flow Poisson Equation • Potential Flow with sources • Heat flow in plate Helmholtz equation – Vibration of plates Numerical Marine Hydrodynamics Lecture 20 2.29
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Partial Differential Equations Elliptic PDEs u ( 0,y)=g 1 (y) Equidistant Sampling Discretization Finite Differences u (
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