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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >P-VERSION LEAST-SQUARES FINITE-ELEMENT FORMULATION FOR AXISYMMETRIC INCOMPRESSIBLE NEWTONIAN AND NON-NEWTONIAN FLUID FLOW WITH HEAT TRANSFER
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P-VERSION LEAST-SQUARES FINITE-ELEMENT FORMULATION FOR AXISYMMETRIC INCOMPRESSIBLE NEWTONIAN AND NON-NEWTONIAN FLUID FLOW WITH HEAT TRANSFER

机译：具有传热的轴对称不可压缩牛顿和非牛顿流体的P版本最小二乘有限元公式

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This article presents a p-version least-squares finite-element formulation for axisymmetric incompressible Newtonian and non-Newtonian fluid flow with heat transfer. The dimensionless form of the equations describing the fluid motion and heat transfer are cast into a set of first-order coupled partial differential equations involving non-Newtonian stresses and heat fluxes as auxiliary variables. The pressure, velocities, stresses, and heat flares are interpolated using equal-order, C-0 continuity, p-version hierarchical approximation functions. The least-squares error functional is constructed using the system of coupled first-order nonlinear partial differential equations without linearization, approximations, or assumptions. The minimization of this least-squares error functional results in a solution vector {delta} that makes the partial derivatives of the error functional with respect to {delta} a null vector. This is accomplished by using Newton's method with a line search. The article presents implementation of the power law model for non-Newtonian viscosity. The fluid properties are also considered to be a function of temperature. Numerical examples are presented to demonstrate the convergence characteristics and the accuracy of the proposed formulation. [References: 40]
机译：本文提出了带有热传递的轴对称不可压缩牛顿和非牛顿流体流动的p版本最小二乘有限元公式。描述流体运动和传热的方程的无量纲形式被转化为一组一阶耦合的偏微分方程，其中涉及非牛顿应力和热通量作为辅助变量。使用等阶的C-0连续性，p版本分层逼近函数对压力，速度，应力和火斑进行插值。最小二乘误差函数是使用没有线性化，近似或假设的耦合的一阶非线性偏微分方程组构造的。该最小二乘方误差函数的最小化导致解向量δ，该向量使误差函数相对于δ的偏导数成为空向量。这是通过将牛顿法与线搜索结合使用来实现的。本文介绍了非牛顿粘度幂律模型的实现。流体性质也被认为是温度的函数。数值算例表明了所提公式的收敛性和准确性。 [参考：40]

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