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# lect_19 - 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 Numerical Marine Hydrodynamics Lecture 19 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 19 2.29 x
Partial Differential Equations Parabolic PDE Heat Flow Equation Insulation Rod x x = L u(L,t)=c 2 x = 0 u(0,t) = c 1 Initial Condition Boundary Conditions IVP in one dimension, BVP in the other κ Thermal conductivity Marching, Explicit or Implicit Schemes σ Specific heat ρ Density u Temperature Numerical Marine Hydrodynamics Lecture 19 2.29

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Partial Differential Equations Parabolic PDE Heat Flow Equation Boundary Conditions Initial Condition σ Insulation Rod u(0,t) = g 1 (t) x = L u(L,t)=g 2 (t) x = 0 Numerical Marine Hydrodynamics Lecture 19 2.29 x
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