lect_19 - Numerical Marine Hydrodynamics Partial...

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Unformatted text preview: 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 Partial Differential Equations A,B and C Constants Hyperbolic Parabolic Elliptic y ( n ) (x,y 2 ) Quasi-linear PDE ( n ) (x 1 ,y) ( n ) (x 2 ,y) ( 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 Thermal conductivity Marching, Explicit or Implicit Schemes Specific heat Density u Temperature Numerical Marine Hydrodynamics Lecture 19 2.29 Partial Differential Equations Parabolic PDE Heat Flow Equation Boundary Conditions Initial Condition 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 Partial Differential Equations Parabolic PDE Equidistant Sampling t Discretization...
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lect_19 - Numerical Marine Hydrodynamics Partial...

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