This paper presents a model for predicting the contaminated mixing volume arising in pipeline batch transfers without physical separators. The proposed technique represents an improvement over the existing methods since it takes into account time-dependent flow rates and accurate concentration-varying axial dispersion coefficients. The governing equation of the model forms a nonlinear boundary-value problem that is solved by a finite element method coupled to the Newton’s method. A comparison among the theoretical predictions of this method, a field test, and other classical procedures show that the proposed method exhibits the best estimate over the whole range of admissible concentrations investigated.
A tetrahedral finite element method of the Hermite type for solving second order elliptic equations in three‐dimension bounded domains is introduced. It is a sort of extension of the Morley triangle [3] but contrary to this element it provides converging approximations in this case. The new element is particularly useful in situations where flux continuity across interelement boundaries is required.
A triangular finite element method of the Hermite type for solving second order elliptic equations in two-dimensional bounded domains is introduced. It can be viewed as a modification of the Morley triangle [8], but contrary to this element it provides converging approximations for this class of problems. The new element is particularly useful in situations where flux or normal stress continuity across interelement boundaries is required.
SUMMARYA computational study of viscous flow between two eccentrically rotating cylinders is presented in which the effect of viscous dissipation is taken into account. The space discretization is based on piecewise linear finite elements with velocity stabilization, while the method of characteristics is used for time integration. Numerical results illustrate the efficiency of the adopted approach.
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