High-order variational multiscale analysis of coupled advective-diffusive-reactive systems

McWilliams, David
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Sahni, Onkar
Shephard, M. S. (Mark S.)
Oberai, Assad
Issue Date
Aeronautical engineering
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A system of advective-diffusive-reactive equations can be used to model many practical problems of interest. In these problems, boundary layer behavior will be present for high Péclet or Damköhler numbers, which may cause the Galerkin method to be unstable. This deficiency can be resolved by using stabilized methods. We first consider a high-order residual-based variational multiscale method based on a single stabilization parameter. Using this method, we find that the optimal convergence rate and nodal exactness are not achieved, especially when the polynomial order of the basis functions is greater than one. More specifically, the convergence rate is not optimal when the order of the basis functions is even. In order to resolve these issues, we derive a high-order variational multiscale method based on multiple stabilization parameters, which models the effect of the fine-scale solution using the fine-scale Green's function. This method achieves the appropriate convergence rate and nodal exactness for a single advective-diffusive-reactive equation.
May 2015
School of Engineering
Dept. of Mechanical, Aerospace, and Nuclear Engineering
Rensselaer Polytechnic Institute, Troy, NY
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