Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume Method
The main aim of this study is to achieve the numerical solution for the Navier–Stokes equations for incompressible, non-turbulent, and subsonic fluid flows with some Gaussian physical uncertainties. The higher-order stochastic finite volume method (SFVM), implemented according to the iterative gener...
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MDPI AG
2025-01-01
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| Series: | Entropy |
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| author | Marcin Kamiński Rafał Leszek Ossowski |
| author_facet | Marcin Kamiński Rafał Leszek Ossowski |
| author_sort | Marcin Kamiński |
| collection | DOAJ |
| description | The main aim of this study is to achieve the numerical solution for the Navier–Stokes equations for incompressible, non-turbulent, and subsonic fluid flows with some Gaussian physical uncertainties. The higher-order stochastic finite volume method (SFVM), implemented according to the iterative generalized stochastic perturbation technique and the Monte Carlo scheme, are engaged for this purpose. It is implemented with the aid of the polynomial bases for the pressure–velocity–temperature (PVT) solutions, for which the weighted least squares method (WLSM) algorithm is applicable. The deterministic problem is solved using the freeware OpenFVM, the computer algebra software MAPLE 2019 is employed for the LSM local fittings, and the resulting probabilistic quantities are computed. The first two probabilistic moments, as well as the Shannon entropy spatial distributions, are determined with this apparatus and visualized in the FEPlot software. This approach is validated using the 2D heat conduction benchmark test and then applied for the probabilistic version of the 3D coupled lid-driven cavity flow analysis. Such an implementation of the SFVM is applied to model the 2D lid-driven cavity flow problem for statistically homogeneous fluid with limited uncertainty in its viscosity and heat conductivity. Further numerical extension of this technique is seen in an application of the artificial neural networks, where polynomial approximation may be replaced automatically by some optimal, and not necessarily polynomial, bases. |
| format | Article |
| id | doaj-art-ebbe93870b2e44e9a81bea11deb3312e |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-ebbe93870b2e44e9a81bea11deb3312e2025-01-24T13:31:53ZengMDPI AGEntropy1099-43002025-01-012716710.3390/e27010067Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume MethodMarcin Kamiński0Rafał Leszek Ossowski1Faculty of Civil Engineering, Architecture and Environmental Engineering, Lodz University of Technology, 90-924 Łódź, PolandFaculty of Civil Engineering, Architecture and Environmental Engineering, Lodz University of Technology, 90-924 Łódź, PolandThe main aim of this study is to achieve the numerical solution for the Navier–Stokes equations for incompressible, non-turbulent, and subsonic fluid flows with some Gaussian physical uncertainties. The higher-order stochastic finite volume method (SFVM), implemented according to the iterative generalized stochastic perturbation technique and the Monte Carlo scheme, are engaged for this purpose. It is implemented with the aid of the polynomial bases for the pressure–velocity–temperature (PVT) solutions, for which the weighted least squares method (WLSM) algorithm is applicable. The deterministic problem is solved using the freeware OpenFVM, the computer algebra software MAPLE 2019 is employed for the LSM local fittings, and the resulting probabilistic quantities are computed. The first two probabilistic moments, as well as the Shannon entropy spatial distributions, are determined with this apparatus and visualized in the FEPlot software. This approach is validated using the 2D heat conduction benchmark test and then applied for the probabilistic version of the 3D coupled lid-driven cavity flow analysis. Such an implementation of the SFVM is applied to model the 2D lid-driven cavity flow problem for statistically homogeneous fluid with limited uncertainty in its viscosity and heat conductivity. Further numerical extension of this technique is seen in an application of the artificial neural networks, where polynomial approximation may be replaced automatically by some optimal, and not necessarily polynomial, bases.https://www.mdpi.com/1099-4300/27/1/67stochastic finite volume methodShannon entropyNavier–Stokes equationsstochastic perturbation technique.cx |
| spellingShingle | Marcin Kamiński Rafał Leszek Ossowski Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume Method Entropy stochastic finite volume method Shannon entropy Navier–Stokes equations stochastic perturbation technique.cx |
| title | Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume Method |
| title_full | Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume Method |
| title_fullStr | Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume Method |
| title_full_unstemmed | Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume Method |
| title_short | Shannon Entropy Computations in Navier–Stokes Flow Problems Using the Stochastic Finite Volume Method |
| title_sort | shannon entropy computations in navier stokes flow problems using the stochastic finite volume method |
| topic | stochastic finite volume method Shannon entropy Navier–Stokes equations stochastic perturbation technique.cx |
| url | https://www.mdpi.com/1099-4300/27/1/67 |
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