English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper presents a new approach to verify accuracy of computationalsimulations. We develop mathematical theorems which can serve as robust aposteriori error estimation techniques to identify numerical pollution, checkthe performance of adaptive meshes, and verify numerical solutions. Wedemonstrate performance of this methodology on problems from flow thoroughporous media. However, one can extend it to other models. We constructmathematical properties such that the solutions to Darcy and Darcy-Brinkmanequations satisfy them. The mathematical properties include the total minimummechanical power, minimum dissipation theorem, reciprocal relation, and maximumprinciple for the vorticity. All the developed theorems have firm mechanicalbases and are independent of numerical methods. So, these can be utilized forsolution verification of finite element, finite volume, finite difference,lattice Boltzmann methods and so forth. In particular, we show that, for agiven set of boundary conditions, Darcy velocity has the minimum totalmechanical power of all the kinematically admissible vector fields. We alsoshow that a similar result holds for Darcy-Brinkman velocity. We then show fora conservative body force, the Darcy and Darcy-Brinkman velocities have theminimum total dissipation among their respective kinematically admissiblevector fields. Using numerical examples, we show that the minimum dissipationand total mechanical power theorems can be utilized to identify pollutionerrors in numerical solutions. The solutions to Darcy and Darcy-Brinkmanequations are shown to satisfy a reciprocal relation, which has the potentialto identify errors in the numerical implementation of boundary conditions.

Mechanics-based solution verification for porous media models