Open AccessFully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations
Author(s) -
Jae-Hong Pyo
Publication year - 2013
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2013/372906
Subject(s) - finite element method , mathematics , boussinesq approximation (buoyancy) , compressibility , gauge (firearms) , space (punctuation) , work (physics) , pressure correction method , projection method , navier–stokes equations , flow (mathematics) , projection (relational algebra) , mixed finite element method , mathematical analysis , convection , natural convection , physics , mathematical optimization , mechanics , geometry , dykstra's projection algorithm , computer science , algorithm , history , archaeology , rayleigh number , thermodynamics , operating system
The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom