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An ill-designed algorithm for solving a multi-dimensional nonlinear diffusion equation in a domain limited by a moving boundary
Deleersnijder, E. (1994). An ill-designed algorithm for solving a multi-dimensional nonlinear diffusion equation in a domain limited by a moving boundary. Math. Comput. Model. 19(10): 75-82
In: Mathematical and Computer Modelling. Elsevier Science: Oxford. ISSN 0895-7177; e-ISSN 1872-9479, more
Peer reviewed article  
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Keywords
    Algorithms
    Equations > Nonlinear equations
    Transport processes > Advection
    Transport processes > Diffusion
    Marine/Coastal
Author  Top 
  • Deleersnijder, E., more
Abstract
    In the Appendix of a recent article, a numerical method was suggested for solving two-dimensional, nonlinear, advection-diffusion equations in a domain limited by a moving boundary. A theoretical analysis reveals that, in most cases, the velocity of the boundary must be predicted to be zero. This undesirable behaviour stems from the incompatibility of the nonlinear numerical stability condition and the criterion allowing the boundary to move. An improvement to the algorithm is briefly outlined.
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