A Numerical Solver for Bugers’ Equations in Two Dimensions
by
Ethan Alan Hereth
University of Central Arkansas
Coauthors: Clarence O. E. Burg

In this presentation we introduce a numerical partial differential equation solver of the following system of Burgers' equations:

∂u/∂t = l₁(∂² u/∂x² + ∂² u/∂y²) + u(∂u/∂x + ∂u/∂y) + f₁(u, v) ∂v/∂x + f₂(u, v) ∂v/∂y

∂v/∂t = l₂(∂² v/∂x² + ∂² v/∂y²) + v(∂v/∂x + ∂v/∂y) + g₁(u, v) ∂u/∂x + g₂(u, v) ∂u/∂y

where the l_is are constants that scale the diffusivity exhibited by the system, while the f_is and g_is are source terms. This code was tested on a decoupled case involving only the convective terms, a decoupled case with diffusion and a case where the system is coupled by setting the f_is and g_is to 1.

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Date received: September 18, 2008