In this paper,we propose and analyze a uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem.Our formulation is based on velocity gradient-velocity-pressure and the resulting scheme ...In this paper,we propose and analyze a uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem.Our formulation is based on velocity gradient-velocity-pressure and the resulting scheme can be flexibly applied to fairly general polygonal meshes.We relax the tangential continuity for velocity,which is the key ingredi-ent in achieving the uniform robustness.We present well-posedness and error analysis for both the semi-discrete scheme and the fully discrete scheme,and the theories indicate that the error estimates for velocity are independent of pressure.Several numerical experiments are presented to confirm the theoretical findings.展开更多
The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and ...The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and attenuation of elastic waves in the porous medium are widely investigated in recent years. However, we have not read any reports on numerical simulation based on the BISQ equation. In this paper, following the BISQ equation, elastic wave propagation in the transversely isotropic porous medium filled with fluids is simulated by the stag-gered grid method for different frequency and phase boundary cases and the two-layer medium. And propagating characteristics of seismic and acoustic waves and various phenomena occured in the propagating process are in-vestigated when the two mechanisms are considered simultaneously.展开更多
The shear-stress transport(SST)turbulence model is incorporated into Navier-Stokes equations to simulate a turbomachinery flowfield.A staggered finite volume method is used to make the mean flow equations and turbulen...The shear-stress transport(SST)turbulence model is incorporated into Navier-Stokes equations to simulate a turbomachinery flowfield.A staggered finite volume method is used to make the mean flow equations and turbulence model equations strongly coupled and enhance the stability of the numerical computation.The implicit treatment of the source terms is applied to the SST model.A steady state solution is obtained using five-stage Runge-Kutta time-stepping scheme with local time stepping and residual smoothing to accelerate convergence. The wall distance d,a key parameter in the SST model,is solved by a partial differential equation.The validations of the code are conducted on rotor 37,wp11 at design and off-design conditions by comparison with measurements and the Spalart-Allmaras(SA)turbulence model.The flow within the tip is calculated with a multi-block grid.展开更多
基金the Hong Kong RGC General Research Fund(Project numbers 14304719 and 14302018)CUHK Faculty of Science Direct Grant 2019-20。
文摘In this paper,we propose and analyze a uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem.Our formulation is based on velocity gradient-velocity-pressure and the resulting scheme can be flexibly applied to fairly general polygonal meshes.We relax the tangential continuity for velocity,which is the key ingredi-ent in achieving the uniform robustness.We present well-posedness and error analysis for both the semi-discrete scheme and the fully discrete scheme,and the theories indicate that the error estimates for velocity are independent of pressure.Several numerical experiments are presented to confirm the theoretical findings.
基金State Natural Sciences Foundation of China (No. 40174012) and the Key Laboratory Foundation of the CNPC (No. GPKL0104).
文摘The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and attenuation of elastic waves in the porous medium are widely investigated in recent years. However, we have not read any reports on numerical simulation based on the BISQ equation. In this paper, following the BISQ equation, elastic wave propagation in the transversely isotropic porous medium filled with fluids is simulated by the stag-gered grid method for different frequency and phase boundary cases and the two-layer medium. And propagating characteristics of seismic and acoustic waves and various phenomena occured in the propagating process are in-vestigated when the two mechanisms are considered simultaneously.
基金supported by the National Natural Science Foundation of China under Contract 50676004 and 50736007
文摘The shear-stress transport(SST)turbulence model is incorporated into Navier-Stokes equations to simulate a turbomachinery flowfield.A staggered finite volume method is used to make the mean flow equations and turbulence model equations strongly coupled and enhance the stability of the numerical computation.The implicit treatment of the source terms is applied to the SST model.A steady state solution is obtained using five-stage Runge-Kutta time-stepping scheme with local time stepping and residual smoothing to accelerate convergence. The wall distance d,a key parameter in the SST model,is solved by a partial differential equation.The validations of the code are conducted on rotor 37,wp11 at design and off-design conditions by comparison with measurements and the Spalart-Allmaras(SA)turbulence model.The flow within the tip is calculated with a multi-block grid.
