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MATLAB Usage

MATLAB can use simbl through MATLAB's built-in Python interface.

Setup

First, make sure simbl is installed in a Python environment:

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pip install similarity-bl

In MATLAB, point pyenv to that Python executable. For example, if simbl is installed in the dev conda environment:

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pyenv("Version", "/opt/miniconda3/envs/dev/bin/python3")

Then import the package:

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simbl = py.importlib.import_module("simbl");

Examples

This example solves an isothermal Mach 5 Falkner-Skan profile, maps the similarity coordinate to physical \(y\), and plots \(u/u_e\) and \(T/T_e\).

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% point MATLAB to the Python environment containing simbl
pyenv("Version", "/opt/miniconda3/envs/dev/bin/python3")

% load simbl
simbl = py.importlib.import_module("simbl");

% define the local similarity problem
inputs = simbl.SimilarityInputs( ...
    pyargs( ...
        "mach_edge", 5.0, ...
        "temp_edge", 220.0, ...
        "temp_wall", 300.0, ...
        "wall_bc", "isothermal" ...
    ) ...
);

% solve the default Falkner-Skan equations
result = simbl.solve_similarity(inputs);
solution = result{1};
info = result{2};

% define dimensional local edge scales for this station
x_station = 0.5;
dens_edge = 0.02;
uvel_edge = 500.0;
visc_edge = 1.5e-5;

% map eta to physical y
y_py = simbl.eta2y( ...
    pyargs( ...
        "eta", solution.eta, ...
        "tau", solution.tau, ...
        "x", x_station, ...
        "dens_edge", dens_edge, ...
        "uvel_edge", uvel_edge, ...
        "visc_edge", visc_edge, ...
        "equations", "falkner_skan" ...
    ) ...
);

% convert Python/NumPy arrays to MATLAB double arrays
eta = double(py.array.array('d', solution.eta.tolist()));
y = double(py.array.array('d', y_py.tolist()));
y_mm = 1000.0 .* y;
uvel = double(py.array.array('d', solution.fp.tolist()));
temp = double(py.array.array('d', solution.tau.tolist()));

% plot profiles
subplot(1, 2, 1)
plot(uvel, y_mm, 'r', 'LineWidth', 2)
grid on
xlabel('u/U_e')
ylabel('y (mm)')
set(gca, 'FontSize', 16)

subplot(1, 2, 2)
plot(temp, y_mm, 'b', 'LineWidth', 2)
grid on
xlabel('T/T_e')
ylabel('y (mm)')
set(gca, 'FontSize', 16)

For swept flows, pass sweep_angle in the inputs and select falkner_skan_cooke in the solver options. The FSC solution includes the crossflow profile solution.g, which is \(w/w_e\). This example also maps the profiles to physical \(y\) for comparison with CFD or experimental data.

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% point MATLAB to the Python environment containing simbl
pyenv("Version", "/opt/miniconda3/envs/dev/bin/python3")

% load simbl
simbl = py.importlib.import_module("simbl");

% define the local swept-flow problem
inputs = simbl.SimilarityInputs( ...
    pyargs( ...
        "mach_edge", 6.0, ...
        "temp_edge", 55.0, ...
        "temp_wall", 300.0, ...
        "wall_bc", "isothermal", ...
        "sweep_angle", 70.0 ...
    ) ...
);

% select the Falkner-Skan-Cooke equation family
options = simbl.SolverOptions( ...
    pyargs( ...
        "equations", "falkner_skan_cooke" ...
    ) ...
);

% solve
result = simbl.solve_similarity(inputs, options);
solution = result{1};
info = result{2};

% define dimensional local edge scales for this station
x_station = 0.5;
dens_edge = 0.02;
uvel_edge = 500.0;
visc_edge = 1.5e-5;

% map eta to physical y
y_py = simbl.eta2y( ...
    pyargs( ...
        "eta", solution.eta, ...
        "tau", solution.tau, ...
        "x", x_station, ...
        "dens_edge", dens_edge, ...
        "uvel_edge", uvel_edge, ...
        "visc_edge", visc_edge, ...
        "equations", "falkner_skan_cooke" ...
    ) ...
);

% convert Python/NumPy arrays to MATLAB double arrays
eta = double(py.array.array('d', solution.eta.tolist()));
y = double(py.array.array('d', y_py.tolist()));
y_mm = 1000.0 .* y;
uvel = double(py.array.array('d', solution.fp.tolist()));
wvel = double(py.array.array('d', solution.g.tolist()));
temp = double(py.array.array('d', solution.tau.tolist()));
dens = 1.0 ./ temp;

% plot streamwise and crossflow profiles
subplot(1, 2, 1)
plot(uvel, y_mm, 'r', 'LineWidth', 2)
grid on
xlabel('u/U_e')
ylabel('y (mm)')
set(gca, 'FontSize', 16)

subplot(1, 2, 2)
plot(wvel, y_mm, 'b', 'LineWidth', 2)
grid on
xlabel('w/W_e')
ylabel('y (mm)')
set(gca, 'FontSize', 16)

Field Names

The common solver output fields are summarized in the Run Solver workflow page.

For density under the constant-pressure boundary-layer approximation, use rho_rhoe = 1.0 ./ temp in MATLAB, where temp is \(T/T_e\).