Grunnleggende konsepter
The author develops a new mixed-VEM for the steady two-dimensional Boussinesq equation with temperature-dependent parameters, utilizing a fixed-point strategy and convergence analysis.
Sammendrag
The content discusses the development of a mixed virtual element method for the Boussinesq problem with temperature-dependent parameters. It includes theoretical analysis, discretization techniques, convergence analysis, and numerical examples to illustrate the proposed method's performance.
Free convection processes are modeled using the Boussinesq approximation, considering fluid properties affected by temperature. Various numerical approximations, including finite element methods and virtual element methods, have been explored in previous studies. The authors propose a fully mixed virtual element method based on pseudostress-velocity formulation for solving the Boussinesq problem with temperature-dependent parameters. The continuous formulation is presented, followed by discretization using virtual element subspaces. Solvability and convergence analyses are conducted to establish optimal error estimates.
Researchers have extended virtual element methods to solve linear and nonlinear problems in fluid mechanics. The proposed method aims to broaden the applicability of mixed-VEM to nonlinear models featuring variable coefficients. By extending previous works on VEMs for fluid mechanics models, the authors introduce a fully mixed VEM for the Boussinesq problem with temperature-dependent parameters.
Statistikk
A priori convergence analysis shows an optimal rate of convergence.
Banach spaces-based approach extended to VEM framework.
Bilinear forms exhibit ellipticity properties.
Constants αS and αT ensure stability conditions are met.
Inf-sup conditions guarantee well-defined operators L_S and L_T.
Estimates show unique solutions exist for uncoupled problems (3.4) and (3.9).
Sitater
"Various types of free convection are present in nature and in industry."
"In recent years, researchers have focused on extending virtual element methods to solve linear and nonlinear problems in fluid mechanics."
"The proposed scheme is rewritten as an equivalent fixed point operator equation."