Simulator

# homemade_conslaws.Simulator — Type.

Simulator{GridType <: Grid, Float <: AbstractFloat}

A type representing a simulation of a conservation law on a grid. The simulation is described by a ConservedSystem and a GridType.

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# homemade_conslaws.simulate! — Method.

simulate!(simulator::Simulator, T, max_dt, callbacks::Vector{Callback}=[]) where Callback

Simulate the system described by simulator until time T using a time step size of at most max_dt. The callbacks are called at each time step. The cell averages are mutated in place.

Example

eq = BurgersEQ()
bc = NeumannBC()

N = 20
x_L, x_R = 0.0, 1.0
x = cell_centers(N, x_L, x_R)
u0(x) = x .< 0.5 ? 1.0 : 0.0
U0 = u0.(x)
grid = UniformGrid1D(N, bc, U0, (x_L, x_R))

F = LaxFriedrichsFlux()
reconstruction = NoReconstruction()
timestepper = ForwardEuler(grid)

system = ConservedSystem(eq, reconstruction, F, timestepper)
simulator = Simulator(system, grid, 0.)

simulate!(simulator, 1., 0.1)

U = cells(grid)

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# homemade_conslaws.simulate_and_aggregate! — Method.

simulate_and_aggregate!(simulator::Simulator, T, max_dt, callbacks::Vector{Callback}=[]) where Callback

The same as simulate! but keeps track of and returns the cell averages and time at each time step.

Example

eq = BurgersEQ()
bc = NeumannBC()

N = 20
x_L, x_R = 0.0, 1.0
x = cell_centers(N, x_L, x_R)
u0(x) = x .< 0.5 ? 1.0 : 0.0
U0 = u0.(x)
grid = UniformGrid1D(N, bc, U0, (x_L, x_R))

F = LaxFriedrichsFlux()
reconstruction = NoReconstruction()
timestepper = ForwardEuler(grid)

system = ConservedSystem(eq, reconstruction, F, timestepper)
simulator = Simulator(system, grid, 0.)

U, t = simulate_and_aggregate!(simulator, 1., 0.1)

u(x, t) = u0(x-0.5t)
Viz.animate_solution(U', u, grid, t, 2)

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# homemade_conslaws.ConservedSystem — Type.

ConservedSystem{EquationType <: Equation, ReconstructionType <: Reconstruction, NumericalFluxType <: NumericalFlux, TimeStepperType <: TimeStepper}

A wrapper around the objects (equation, reconstruction, numerical flux, and time stepper) needed to solve a conservation law.

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