1. An energy-preserving unconditionally stable fractional step method on collocated grids
- Author
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Santos Serrano, Daniel, Trias Miquel, Francesc Xavier, Colomer Rey, Guillem, Pérez Segarra, Carlos David, Universitat Politècnica de Catalunya. Doctorat en Enginyeria Tèrmica, Universitat Politècnica de Catalunya. Departament de Màquines i Motors Tèrmics, Universitat Politècnica de Catalunya. Centre Tecnològic de la Transferència de Calor, and Universitat Politècnica de Catalunya. CTTC - Centre Tecnològic de Transferència de Calor
- Subjects
FVM ,Collocated ,Unconditionally stable ,FSM ,Energy-preserving ,Symmetry-preserving ,Física::Termodinàmica [Àrees temàtiques de la UPC] ,Dinàmica de fluids computacional ,Computational fluid dynamics ,Energy conservation ,Energia--Estalvi - Abstract
Preservation of energy is fundamental in order to avoid the introduction of unphysical energy that can lead to unstable simulations. In this work, an energy-preserving unconditionally stable fractional step method on collocated grids is presented as a method which guarantees both preservation of energy and stability of our simulation. Using an algebraic (matrix-vector) representation of the classical incompressible Navier-Stokes equations mimicking the continuous properties of the differential operators, conservation of energy is formally proven. Furthermore, the appearence of unphysical velocities in highly distorted meshes is also adressed. This problem comes from the interpolation of the pressure gradient from faces to cells in the velocity correction equation, and can be corrected by using a proper interpolation. This work has been financially supported by the project RETOtwin [PDC2021-120970-I00] funded by MCIN/AEI/10.13039/501100011033 and European Union Next Generation EU/PRTR. D. Santos acknowledges a FI AGAUR-Generalitat de Catalunya fellowship (2020FI B 00839). The authors thankfully acknowledge these institutions.
- Published
- 2022
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