Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Numerical simulation of compressible and incompressible Newtonian flows using a total Lagrangian position-based finite element formulation
Submission Author:
Péricles Rafael Pavão Carvalho , MA , Brazil
Co-Authors:
Péricles Rafael Pavão Carvalho, Giovane Avancini, Rodolfo Sanches
Presenter: Péricles Rafael Pavão Carvalho
doi://10.26678/ABCM.COBEM2023.COB2023-2196
Abstract
We present a position-based finite element formulation for solving free-surface Newtonian fluid-flow problems using a total Lagrangian description. This formulation was already applied to incompressible Newtonian flows in previous works, and is extended to temperature-independent compressible cases in this work, allowing a comparison in terms of implementation and results, particularly for problems with moderate values of bulk modulus. To separate the volumetric and isochoric effects of the constitutive model, we apply the multiplicative decomposition of the deformation gradient. The employed approach differs from traditional fluid methods by using positions as nodal parameters of the system, instead of velocities. The compressible model has the advantage of not requiring additional pressure degrees of freedom in the global system. However, it can lead to numerical instabilities and convergence problems for large values of bulk modulus if no stabilization methods are applied. In order to evaluate the advantages and limitations of the model, a representative benchmark example is simulated, using different meshes and bulk modulus values. The obtained results are consistent, showing similarities between the compressible and incompressible models for moderate values of bulk modulus. However, to extend the formulation to quasi-incompressible models and allow larger values of bulk modulus without numerical instability issues, further implementations are required regarding numerical stabilization methods.
Keywords
Lagrangian, fluid, compressible, Incompressible, Finite Element Method, position-based, Newtonian
