The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simu...The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.展开更多
This paper presents an effective discretization scheme for approximating convective transport. The discretization scheme, the weighted second upwind and central differencing (WSUC) scheme, uses weighted second order u...This paper presents an effective discretization scheme for approximating convective transport. The discretization scheme, the weighted second upwind and central differencing (WSUC) scheme, uses weighted second order upwind and central differencing. The theoretical analysis shows that the WSUC scheme is total variation bounded and unconditionally stable for convective numerical stability. Two numerical tests show that the WSUC scheme is more accurate and has higher resolution than the first order upwind scheme, a second order upwind scheme, the SOUCUP scheme and the MSOUCUP scheme. As an example, the thermal stratification in a thermal storage tank is calculated using the WSUC scheme.展开更多
基金supported by the Iraqi ministry of higher education and scientific research
文摘The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.
文摘This paper presents an effective discretization scheme for approximating convective transport. The discretization scheme, the weighted second upwind and central differencing (WSUC) scheme, uses weighted second order upwind and central differencing. The theoretical analysis shows that the WSUC scheme is total variation bounded and unconditionally stable for convective numerical stability. Two numerical tests show that the WSUC scheme is more accurate and has higher resolution than the first order upwind scheme, a second order upwind scheme, the SOUCUP scheme and the MSOUCUP scheme. As an example, the thermal stratification in a thermal storage tank is calculated using the WSUC scheme.
