GVF - integrating the backwater curve

what are the 3 common numerical integration methods used for solving the GVF equation?

• direct step method, solve for dy or dx

• standard step method, solve for depth dy using dEs/dx = S₀-S_f

• numerical integration

what direction does the integration proceed in if flow is a) supercritical and b)subcritical

a) forward in x (upstream control)

b) backward in x (downstream control)

describe the direct step method

a) solve for depth y at a fixed distance intervals Δx

b) solve for distance x at a fixed height/depth intervals Δy

describe the standard step method

• solves for depth y at specified distances x, intervals Δx

• requires iterative solutions at each step so is better suited to a computer programme rather than hand calcualtions