New Schemes, Positive Definiteness and Energy Preserving Approaches for Oldroyd-B Model Under Slip Boundary Condition

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Abstract: New numerical schemes for simulating the Oldroyd-B model are formulated and analyzed. The first approach is based on the semi-implicit Euler scheme, while the second method applies the Marchuk-Yanenko splitting scheme. The goal is to develop schemes that preserve the symmetry and positive definiteness of the conformation tensor, as well as the energy estimate, which includes kinetic energy and the elastic energy of the extra stress, as previously obtained by A. Lozinski and R. Owens in J. Non-Newtonian Fluid Mech., 112, 161–176, 2003. We finally present numerical results which are consistent with theoretical predictions.

International Journal of Applied Mathematics, Computational Science and Systems Engineering, E-ISSN: 2766-9823, Volume 7, 2025, Art. #1

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J. K. Djoko, J. Koko, T. Sayah, "New Schemes, Positive Definiteness and Energy Preserving Approaches for Oldroyd-B Model Under Slip Boundary Condition," International Journal of Applied Mathematics, Computational Science and Systems Engineering, vol. 7, pp. 1-18, 2025, DOI:10.37394/232026.2025.7.1
J. K. Djoko, J. Koko, T. Sayah. New Schemes, Positive Definiteness and Energy Preserving Approaches for Oldroyd-B Model Under Slip Boundary Condition. International Journal of Applied Mathematics, Computational Science and Systems Engineering. 2025;7:1-18. 10.37394/232026.2025.7.1
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