In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows...In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.展开更多
The proposed SUPG/PSPG stabilized FEM formulation for incompressible fluid flow simulation is extended to thermo-magnetically driven flows, and is used for the calculation of the direct and sensitivity thermal,fluid f...The proposed SUPG/PSPG stabilized FEM formulation for incompressible fluid flow simulation is extended to thermo-magnetically driven flows, and is used for the calculation of the direct and sensitivity thermal,fluid flow and electric potential fields. The method is demonstrated through the solution of an inverse problem with known results.展开更多
In this paper,a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin(SUPG)virtual element method(VEM)discretization of convection dominated diffusion equation.A global upp...In this paper,a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin(SUPG)virtual element method(VEM)discretization of convection dominated diffusion equation.A global upper bound and a local lower bound for the a posteriori error estimates are derived in the natural SUPG norm,where the global upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual element discretization errors.Based on the Dörfler’s marking strategy,adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal meshes.Numerical experiments show the robustness of the a posteriori error estimates.展开更多
文摘In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.
基金Sponsored by the Heilongjiang Provincial Natural Science Foundation(Grant No. F0215)Heilongjiang Provincial Science Foundation for Youth (Grant No. QC03C03)
文摘The proposed SUPG/PSPG stabilized FEM formulation for incompressible fluid flow simulation is extended to thermo-magnetically driven flows, and is used for the calculation of the direct and sensitivity thermal,fluid flow and electric potential fields. The method is demonstrated through the solution of an inverse problem with known results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11971276,11301311)by the Natural Science Foundation of Shandong Province(Grant No.ZR2016JL004).
文摘In this paper,a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin(SUPG)virtual element method(VEM)discretization of convection dominated diffusion equation.A global upper bound and a local lower bound for the a posteriori error estimates are derived in the natural SUPG norm,where the global upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual element discretization errors.Based on the Dörfler’s marking strategy,adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal meshes.Numerical experiments show the robustness of the a posteriori error estimates.
