The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flo...The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.展开更多
A new finite difference scheme-SCSD scheme has been proposed based on CD (Central Difference)scheme and SUD (Secondr-order Upwind Difference) scheme. Its basic feature is controIlable convectivesfability and always se...A new finite difference scheme-SCSD scheme has been proposed based on CD (Central Difference)scheme and SUD (Secondr-order Upwind Difference) scheme. Its basic feature is controIlable convectivesfability and always second-order accuracy (Stability-Controllable Second-order Difference ). It hasbeen proven that this scheme is convective-stable if the grid Peclet number .The advanage of this new scheme has been discussed based on the modified wavenumber analysis byusing Fourier transform. This scheme has been applied to the 2-D incompressible convective-diffusiveequation and 2-D compressible Euler equation, and corresponding finite difference equations have beenderived. Numerical examples of 1-D Burgers equation and 2-D transport equation have been presentedto show its good accuracy and controllable convective stability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 National Basic Research Program of China (Grant No. 2006CB605205)the National Natural Science Foundation of China (Grant Nos. 10672019 and 10572062)the Science and Technology Foundation of Shanghai (Grant No. 055207081)
文摘The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.
文摘A new finite difference scheme-SCSD scheme has been proposed based on CD (Central Difference)scheme and SUD (Secondr-order Upwind Difference) scheme. Its basic feature is controIlable convectivesfability and always second-order accuracy (Stability-Controllable Second-order Difference ). It hasbeen proven that this scheme is convective-stable if the grid Peclet number .The advanage of this new scheme has been discussed based on the modified wavenumber analysis byusing Fourier transform. This scheme has been applied to the 2-D incompressible convective-diffusiveequation and 2-D compressible Euler equation, and corresponding finite difference equations have beenderived. Numerical examples of 1-D Burgers equation and 2-D transport equation have been presentedto show its good accuracy and controllable convective stability
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.
