| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Sao Paulo, Dept Matemat Aplicada & Estat, Inst Ciencias Matemat & Comp ICMC, Campus Sao Carlos, BR-1025480 Sao Paulo, SP - Brazil
[2] Kanazawa Univ, Fac Math & Phys, Kanazawa, Ishikawa 9201192 - Japan
[3] Univ Estadual Paulista, Dept Matemat & Comp, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | SIAM JOURNAL ON NUMERICAL ANALYSIS; v. 59, n. 6, p. 2955-2988, 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
In this work, new finite difference schemes are presented for dealing with the upper convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the constitutive equation of the popular viscoelastic models, is reformulated in order to obtain approximations of second-order in time for solving a simplified constitutive equation in one and two dimensions. The theoretical analysis of the truncation errors of the methods takes into account the linear and quadratic interpolation operators based on a Lagrangian framework. Numerical experiments illustrating the theoretical results for the model equation defined in one and two dimensions are included. Finally, the finite difference approximations of second-order in time are also applied for solving a two-dimensional Oldroyd-B constitutive equation subjected to a prescribed velocity field at different Weissenberg numbers. (AU) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 17/11428-2 - Numerical Methods for Non-Newtonian Free Surface Flows: effects of surface tension |
| Grantee: | Débora de Oliveira Medeiros |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 19/08742-2 - Stabilization schemes for solving viscoelastic free surface flows with surface tension effects |
| Grantee: | Débora de Oliveira Medeiros |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |