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Award ID contains: 2110379

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  1. ; ; (, Numerical Methods for Partial Differential Equations)
    ABSTRACT In 1991 Ramshaw and Mesina proposed a novel synthesis of penalty methods and artificial compression methods. When the two were balanced they found the combination was 3–4 orders more accurate than either alone. This report begins developing a mathematical foundation addressing the reliability of their interesting method. We perform stability analysis, semi‐discrete error analysis, and tests of the algorithm. 
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  2. ; (, Numerical Methods for Partial Differential Equations)
    Abstract The classical Smagorinsky model's solution is an approximation to a (resolved) mean velocity. Since it is an eddy viscosity model, it cannot represent a flow of energy from unresolved fluctuations to the (resolved) mean velocity. This model has recently been corrected to incorporate this flow and still be well‐posed. Herein we first develop some basic properties of the corrected model. Next, we perform a complete numerical analysis of two algorithms for its approximation. They are tested and proven to be effective. 
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  3. ; ; ; (, Numerical Methods for Partial Differential Equations)
    Abstract Artificial compression methods are used in computational fluid dynamics as a cost‐effective way of solving for the velocity and pressure in a flow. However, relaxation of compressibility in these algorithms yields nonphysical oscillations in the pressure. This report presents analysis and computational tests of time filters to reduce nonphysical acoustic waves in artificial compression methods. 
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  4. (, SeMA Journal)
    Free, publicly-accessible full text available May 26, 2026
  5. ; ; (, Physica D: Nonlinear Phenomena)
    Free, publicly-accessible full text available January 1, 2026
  6. ; (, Applied Mathematics Letters)
    Full Text Available 
  7. ; (, International Journal of Numerical Analysis and Modeling)
    Full Text Available 
  8. ; ; (, Advances in Computational Science and Engineering)
    Full Text Available 
  9. ; (, Journal of Mathematical Analysis and Applications)
    Full Text Available 
  10. ; ; (, International journal of numerical analysis and modeling)
    Accepted Manuscript Full Text Available