Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials
This paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–Stokes equations in a strong formulation. The soluti...
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MDPI AG
2021-10-01
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| Online Access: | https://www.mdpi.com/1996-1944/14/20/6210 |
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| author | Martina Bašić Branko Blagojević Chong Peng Josip Bašić |
| author_facet | Martina Bašić Branko Blagojević Chong Peng Josip Bašić |
| author_sort | Martina Bašić |
| collection | DOAJ |
| description | This paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–Stokes equations in a strong formulation. The solution is obtained using a split-step scheme, i.e., by decoupling the solutions of the pressure and velocity. The pressure is obtained by solving a Poisson equation, and the velocity is solved in a semi-implicit formulation. The matrix-free solution to the equations, and Lagrangian advection of mesh-free nodes allowed for a fully parallelized implementation on the CPU and GPU, which ensured an affordable computing time and large time steps. A set of four benchmarks are presented to demonstrate the robustness and accuracy of the proposed formulation. The tested two- and three-dimensional simulations used Power Law, Casson and Bingham models. An Abram slump test and a dam break test were performed using the Bingham model, yielding visual and numerical results in accordance with the experimental data. A square lid-driven cavity was tested using the Casson model, while the Power Law model was used for a skewed lid-driven cavity test. The simulation results of the lid-driven cavity tests are in good agreement with velocity profiles and stream lines of published reports. A fully implicit scheme will be introduced in future work. As the method precisely reproduces the pressure field, non-Newtonian models that strongly depend on the pressure will be validated. |
| first_indexed | 2024-03-10T06:25:07Z |
| format | Article |
| id | doaj.art-99e380128f2a465cbb638cd0e76840cd |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T06:25:07Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-99e380128f2a465cbb638cd0e76840cd2023-11-22T19:00:54ZengMDPI AGMaterials1996-19442021-10-011420621010.3390/ma14206210Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian MaterialsMartina Bašić0Branko Blagojević1Chong Peng2Josip Bašić3Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R. Boškovića 32, 21000 Split, CroatiaFaculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R. Boškovića 32, 21000 Split, CroatiaInstitute of Geotechnical Engineering, University of Natural Resources and Life Sciences Vienna, Feistmantelstraße 4, 1180 Wien, AustriaFaculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R. Boškovića 32, 21000 Split, CroatiaThis paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–Stokes equations in a strong formulation. The solution is obtained using a split-step scheme, i.e., by decoupling the solutions of the pressure and velocity. The pressure is obtained by solving a Poisson equation, and the velocity is solved in a semi-implicit formulation. The matrix-free solution to the equations, and Lagrangian advection of mesh-free nodes allowed for a fully parallelized implementation on the CPU and GPU, which ensured an affordable computing time and large time steps. A set of four benchmarks are presented to demonstrate the robustness and accuracy of the proposed formulation. The tested two- and three-dimensional simulations used Power Law, Casson and Bingham models. An Abram slump test and a dam break test were performed using the Bingham model, yielding visual and numerical results in accordance with the experimental data. A square lid-driven cavity was tested using the Casson model, while the Power Law model was used for a skewed lid-driven cavity test. The simulation results of the lid-driven cavity tests are in good agreement with velocity profiles and stream lines of published reports. A fully implicit scheme will be introduced in future work. As the method precisely reproduces the pressure field, non-Newtonian models that strongly depend on the pressure will be validated.https://www.mdpi.com/1996-1944/14/20/6210non-NewtonianrheologyLagrangianmeshlessLDDCasson |
| spellingShingle | Martina Bašić Branko Blagojević Chong Peng Josip Bašić Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials Materials non-Newtonian rheology Lagrangian meshless LDD Casson |
| title | Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials |
| title_full | Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials |
| title_fullStr | Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials |
| title_full_unstemmed | Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials |
| title_short | Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials |
| title_sort | lagrangian differencing dynamics for time independent non newtonian materials |
| topic | non-Newtonian rheology Lagrangian meshless LDD Casson |
| url | https://www.mdpi.com/1996-1944/14/20/6210 |
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