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Preliminary tests of a hybrid numerical-asymptotic method for solving nonlinear advection-diffusion equations in a domain limited by a self-adjusting boundary
Deleersnijder, E.; Roland, M. (1993). Preliminary tests of a hybrid numerical-asymptotic method for solving nonlinear advection-diffusion equations in a domain limited by a self-adjusting boundary. Math. Comput. Model. 17(12): 35-47
In: Mathematical and Computer Modelling. Elsevier Science: Oxford; New York. ISSN 0895-7177, more
Peer reviewed article  

Available in Authors 

Keywords
    Advection; Diffusion; Equations; Hybrids; Nonlinear; Nonlinear equations; Tests; Marine

Authors  Top 
  • Deleersnijder, E., more
  • Roland, M.

Abstract
    An advection-diffusion equation is examined in which the diffusion coefficient is proportional to a positive power of the dependent variable, h. Because the diffusion coefficient is zero where h is zero, it is believed that the domain where h ? 0 expands at a finite velocity, u?, which must be calculated in an appropriate way if an accurate numerical solution technique is to be implemented. An asymptotic study leads to a local approximation of u?. The latter is then utilized in a finite volume solution of an axisymmetric problem where an exact solution can be obtained. The accuracy of the numerical results is excellent. Some peculiarities of the numerical solution are highlighted, and it is shown that they are due to the simplistic nature of the axisymmetric problem solved, which may be partly responsible for the high quality of the numerical results. Although the preliminary results are very encouraging, further testing of the method is needed, especially in fully two-dimensional cases.

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