针对一维带有不连续系数和奇异源项的椭圆型方程,采用匹配界面和边界(MIB,matched interface and boundary)方法进行求解.该方法对微分方程和跳跃条件的离散是分别进行的,通过在界面附近构造虚拟点达到提高差分格式整体精度的目的,文中...针对一维带有不连续系数和奇异源项的椭圆型方程,采用匹配界面和边界(MIB,matched interface and boundary)方法进行求解.该方法对微分方程和跳跃条件的离散是分别进行的,通过在界面附近构造虚拟点达到提高差分格式整体精度的目的,文中对Neumann边界也给出了处理办法.通过数值算例对文中构造的差分方法进行了验证,并与文献中的浸入界面方法进行了对比,数值结果证明了方法的有效性和可行性.展开更多
A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) is...A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) isothermal walls where the temperatures of the plates are equal and constant and(b) with constant but different plate temperatures.The Knudsen number is Kn 0.1,which corresponds to the slip and continuum flow.The flow is defined by continuity,Navier-Stokes and energy continuum equations,along with the velocity slip and the temperature jump first order boundary conditions.An analytical solution for velocity and temperature is obtained by developing a perturbation scheme.The first approximation corresponds to the continuum flow conditions,while the others represent the contribution of the rarefaction effect.In addition,a numerical solution of the problems is given to confirm the accuracy of the analytical results.The exact analytical solution,for constant viscosity and conductivity is found for the isothermal walls case as well.It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.展开更多
文摘针对一维带有不连续系数和奇异源项的椭圆型方程,采用匹配界面和边界(MIB,matched interface and boundary)方法进行求解.该方法对微分方程和跳跃条件的离散是分别进行的,通过在界面附近构造虚拟点达到提高差分格式整体精度的目的,文中对Neumann边界也给出了处理办法.通过数值算例对文中构造的差分方法进行了验证,并与文献中的浸入界面方法进行了对比,数值结果证明了方法的有效性和可行性.
基金supported by the Ministry of Science of the Republic of Serbia (Grant No.174014)
文摘A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) isothermal walls where the temperatures of the plates are equal and constant and(b) with constant but different plate temperatures.The Knudsen number is Kn 0.1,which corresponds to the slip and continuum flow.The flow is defined by continuity,Navier-Stokes and energy continuum equations,along with the velocity slip and the temperature jump first order boundary conditions.An analytical solution for velocity and temperature is obtained by developing a perturbation scheme.The first approximation corresponds to the continuum flow conditions,while the others represent the contribution of the rarefaction effect.In addition,a numerical solution of the problems is given to confirm the accuracy of the analytical results.The exact analytical solution,for constant viscosity and conductivity is found for the isothermal walls case as well.It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.
