A new transformation of Burger’s equation for an exact solution in a bounded region necessary for certain boundary conditions |
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Authors: | DO Besong |
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Institution: | Independent Researcher, 3 McIntosh House, Millender Walk, London SE16 2BJ, UK |
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Abstract: | In this work, the transient analytic solution is found for the initial-boundary-value Burgers equation in 0?x?L. The boundary conditions are a homogeneous Dirichlet condition at x=0 and a constant total flux at x=L. The technique used consists of applying the transformation that reduces Burgers equation to a linear diffusion-advection equation. Previous work on this equation in a bounded region has only applied the Cole-Hopf transformation , which transforms Burgers equation to the linear diffusion equation. The Cole-Hopf transformation can only solve Burgers equation with constant Dirichlet boundary conditions, or time-dependent Dirichlet boundary conditions of the form u(0,t)=F1(t) and u(L,t)=F2(t),0?x?L. In this work, it is shown that the Cole-Hopf transformation will not solve Burgers equation in a bounded region with the boundary conditions dealt with in this work. |
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Keywords: | Burgers equation with Robin boundary Exact solution of Burgers equation Cole-Hopf-type transformation Limitations of the Cole-Hopf transformation Exact solution to Burgers equation |
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