class FirstOrderPDE extends Error
The FirstOrderPDE
class is used to solve first order partial differential
equations like the Advection Equation. Let 'u(x, t)' = concentration in a fluid
with velocity 'v' at position '0 <= x <= xm' and time 't' > 0. Numerically solve the
Advection Equation: u_t + v(x, t) * u_x = 0 with initial conditions u(x, 0) = ic(x) boundary conditions (u(0, t), u(xm, t)) = bc
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new
FirstOrderPDE(v: (Double, Double) ⇒ Double, dt: Double, dx: Double, xm: Double, ic: FunctionS2S, bc: (Double, Double))
- v
the velocity field function v(x, t)
- dt
delta 't'
- dx
delta 'x'
- xm
the length of the column
- ic
the initial conditions as a function of position 'x'
- bc
the boundary conditions as a 2-tuple for end-points 0 and 'xm'
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def
solve(te: Double): VectorD
Solve for the concentration of the column at time t, returning the vector of concentration representing the concentration profile of column over its length.
Solve for the concentration of the column at time t, returning the vector of concentration representing the concentration profile of column over its length. This method uses an explicit finite difference technique to solve the PDE. L-W is the Lax-Wendroff scheme which has second-order accuracy.
- te
the time the solution is desired (t-end)
- See also
math.nju.edu.cn/~qzh/numPDE.pdf
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