Scheda di dettaglio – i prodotti della ricerca
| Dato | Valore |
|---|---|
| Title | A QUADRATURE-BASED SCHEME FOR NUMERICAL SOLUTIONS TO KIRCHHOFF TRANSFORMED RICHARDS' EQUATION |
| Abstract | In this work we propose a new numerical scheme for solving Richards' equation within Gardner's framework and accomplishing mass conservation. In order to do so, we resort to Kirchhoff transformation of Richards' equation in mixed form, so to exploit specific Gardner model features, obtaining a linear second order partial differential equation. Then, leveraging the mass balance condition, we integrate both sides of the equation over a generic grid cell and discretize integrals using trapezoidal rule. This approach provides a linear non-homogeneous initial value problem with respect to the Kirchhoff transform variable, whose solution yields the sought numerical scheme. Such a scheme is proven to be l2-stable and convergent to the exact solution under suitably conditions on step-sizes, retaining the order of convergence from the underlying quadrature formula. |
| Source | Journal of computational dynamics (Print) 9 (2), pp. 69–84 |
| Keywords | Richards' equationKirchhoff transformationmass balance conditionGardner's constitutive relationsunsaturated flow model |
| Journal | Journal of computational dynamics (Print) |
| Editor | American Institute of Mathematical Sciences, Springfield MO, Stati Uniti d'America |
| Year | 2022 |
| Type | Articolo in rivista |
| DOI | 10.3934/jcd.2022001 |
| Authors | Berardi, Marco; Difonzo, Fabio, V |
| Text | 478385 2022 10.3934/jcd.2022001 ISI Web of Science WOS 000757494500001 Richards equation Kirchhoff transformation mass balance condition Gardner s constitutive relations unsaturated flow model A QUADRATURE BASED SCHEME FOR NUMERICAL SOLUTIONS TO KIRCHHOFF TRANSFORMED RICHARDS EQUATION Berardi, Marco; Difonzo, Fabio, V Ist Ric Acque; Univ Bari Aldo Moro In this work we propose a new numerical scheme for solving Richards equation within Gardner s framework and accomplishing mass conservation. In order to do so, we resort to Kirchhoff transformation of Richards equation in mixed form, so to exploit specific Gardner model features, obtaining a linear second order partial differential equation. Then, leveraging the mass balance condition, we integrate both sides of the equation over a generic grid cell and discretize integrals using trapezoidal rule. This approach provides a linear non homogeneous initial value problem with respect to the Kirchhoff transform variable, whose solution yields the sought numerical scheme. Such a scheme is proven to be l2 stable and convergent to the exact solution under suitably conditions on step sizes, retaining the order of convergence from the underlying quadrature formula. 9 Published version A quadrature based scheme for numerical solutions to Kirchhoff transformed Richards equation 10.3934_jcd.2022001.pdf Articolo in rivista American Institute of Mathematical Sciences 2158 2491 Journal of computational dynamics Print Journal of computational dynamics Print Journal of computational dynamics J. comput. dyn. Print JCD marco.berardi BERARDI MARCO |