象山港是一具有广阔潮滩和大潮差区域的半封闭型海湾,进行数值模拟时必须引入动边界技术来考虑露漫滩的影响。在二维模式中引入动边界技术相对成熟一些,而将这些二维模式使用的露漫滩处理方法简单地搬入三维模式中,常遇到由于边界不连...象山港是一具有广阔潮滩和大潮差区域的半封闭型海湾,进行数值模拟时必须引入动边界技术来考虑露漫滩的影响。在二维模式中引入动边界技术相对成熟一些,而将这些二维模式使用的露漫滩处理方法简单地搬入三维模式中,常遇到由于边界不连续变动而产生的数值"噪音"及计算不稳定现象。原始POM(Princeton ocean model)模型采用固定边界,没有使用动边界技术,故无法模拟漫滩流。借鉴BURCHARD et al 2004年的研究工作,在原始POM模型的基础上,突破其为固定边界模式的局限,基于尽量使模式物理上满足流动简化需要的原则,引入了一种较为自然的动边界处理技术,使得在非常浅水处和复杂的地形情况下,应用合理的数学表达式体现该物理过程。当总水深大于设定的临界水深时,体现的数学方程是通常形式的动量方程;而当总水深接近设定的最小允许水深时,模型的动量方程被简化为变化率、摩擦力和正压梯度等项之间的平衡关系,此时由于摩擦力占优,相应的流速也会趋于0,这样可以有效避免计算中出现负水深。除在非常浅水处对动量方程作简化外,对于陡坡地形附近的露漫滩问题,当发生一个网格点上的水位低于相邻格点海床的现象时,还需对正压梯度的求解作一个简单的数值处理,以避免不合理值的出现。此外,通过修改原始POM模型的底摩擦系数表达式,可使模型在模拟露漫滩过程时计算更加稳定。改进后的POM模型被用来模拟象山港海域内的三维潮流场,模型计算结果与2个潮位站、1个锚系站和2个船测连续站资料进行了比较,符合良好。整个模型很好地再现了象山港内大区域三维涨、落潮流特征和变化规律,同时象山港顶区域涨憩、落急、落憩和涨急4个特征时刻的流场水平和垂直分布变化过程反映该模型能很好地反映涨、落潮造成的潮间带的露漫滩过程,由此说�展开更多
The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotrop...The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)additionally.Since a(x,t)may be degenerate on the parabolic boundary∂Ω×(0,T),instead of the boundedness of the gradient|∇u|for the usual porous medium,we can only show that∇u∈L^(∞)(0,T;L^(2)_(loc)(Ω)).Based on this property,the partial boundary value conditions matching up with the anisotropic porous medium equation are discovered and two stability theorems of weak solutions can be proved naturally.展开更多
The dynamics of a solid spherical body in an oscillating liquid flow in a vertical axisymmetric channel of variable cross section is experimentally studied.It is shown that the oscillating liquid leads to the generati...The dynamics of a solid spherical body in an oscillating liquid flow in a vertical axisymmetric channel of variable cross section is experimentally studied.It is shown that the oscillating liquid leads to the generation of intense averaged flows in each of the channel segments.The intensity and direction of these flows depend on the dimensionless oscillating frequency.In the region of studied frequencies,the dynamics of the considered body is examined when the primary vortices emerging in the flow occupy the whole region in each segment.For a fixed frequency,an increase in the oscillation amplitude leads to a phase-inclusion holding effect,i.e.,the body occupies a quasi-stationary position in one of the cells of the vertical channel,while oscillating around its average position.It is also shown that the oscillating motion of a liquid column generates an averaged force acting on the body,the magnitude of which depends on the properties of the body and its position in the channel.The quasi-stationary position is determined by the relative density and size of the body,as well as the dimensionless frequency.The behavior of the body as a function of the amplitude and frequency of fluid oscillation and relative size is discussed in detail.Such findings may be used in the future to control the position of a phase inclusion and/or to strengthen mass transfer effects in a channel of variable cross section by means of fluid oscillations.展开更多
文摘象山港是一具有广阔潮滩和大潮差区域的半封闭型海湾,进行数值模拟时必须引入动边界技术来考虑露漫滩的影响。在二维模式中引入动边界技术相对成熟一些,而将这些二维模式使用的露漫滩处理方法简单地搬入三维模式中,常遇到由于边界不连续变动而产生的数值"噪音"及计算不稳定现象。原始POM(Princeton ocean model)模型采用固定边界,没有使用动边界技术,故无法模拟漫滩流。借鉴BURCHARD et al 2004年的研究工作,在原始POM模型的基础上,突破其为固定边界模式的局限,基于尽量使模式物理上满足流动简化需要的原则,引入了一种较为自然的动边界处理技术,使得在非常浅水处和复杂的地形情况下,应用合理的数学表达式体现该物理过程。当总水深大于设定的临界水深时,体现的数学方程是通常形式的动量方程;而当总水深接近设定的最小允许水深时,模型的动量方程被简化为变化率、摩擦力和正压梯度等项之间的平衡关系,此时由于摩擦力占优,相应的流速也会趋于0,这样可以有效避免计算中出现负水深。除在非常浅水处对动量方程作简化外,对于陡坡地形附近的露漫滩问题,当发生一个网格点上的水位低于相邻格点海床的现象时,还需对正压梯度的求解作一个简单的数值处理,以避免不合理值的出现。此外,通过修改原始POM模型的底摩擦系数表达式,可使模型在模拟露漫滩过程时计算更加稳定。改进后的POM模型被用来模拟象山港海域内的三维潮流场,模型计算结果与2个潮位站、1个锚系站和2个船测连续站资料进行了比较,符合良好。整个模型很好地再现了象山港内大区域三维涨、落潮流特征和变化规律,同时象山港顶区域涨憩、落急、落憩和涨急4个特征时刻的流场水平和垂直分布变化过程反映该模型能很好地反映涨、落潮造成的潮间带的露漫滩过程,由此说�
基金supported by Natural Science Foundation of Fujian Province(No.2022J011242),China。
文摘The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)additionally.Since a(x,t)may be degenerate on the parabolic boundary∂Ω×(0,T),instead of the boundedness of the gradient|∇u|for the usual porous medium,we can only show that∇u∈L^(∞)(0,T;L^(2)_(loc)(Ω)).Based on this property,the partial boundary value conditions matching up with the anisotropic porous medium equation are discovered and two stability theorems of weak solutions can be proved naturally.
文摘The dynamics of a solid spherical body in an oscillating liquid flow in a vertical axisymmetric channel of variable cross section is experimentally studied.It is shown that the oscillating liquid leads to the generation of intense averaged flows in each of the channel segments.The intensity and direction of these flows depend on the dimensionless oscillating frequency.In the region of studied frequencies,the dynamics of the considered body is examined when the primary vortices emerging in the flow occupy the whole region in each segment.For a fixed frequency,an increase in the oscillation amplitude leads to a phase-inclusion holding effect,i.e.,the body occupies a quasi-stationary position in one of the cells of the vertical channel,while oscillating around its average position.It is also shown that the oscillating motion of a liquid column generates an averaged force acting on the body,the magnitude of which depends on the properties of the body and its position in the channel.The quasi-stationary position is determined by the relative density and size of the body,as well as the dimensionless frequency.The behavior of the body as a function of the amplitude and frequency of fluid oscillation and relative size is discussed in detail.Such findings may be used in the future to control the position of a phase inclusion and/or to strengthen mass transfer effects in a channel of variable cross section by means of fluid oscillations.
