CAJ | 학술논문

寻找一种高精度的空间单元插值模式是数值求解三维对流问题的关键.在前人研究的基础上,探讨了一种任意空间六面体的拟协调单元,保证节点上的物理量函数及其一阶导数连续.算例表明,该方法具有良好的计算稳定性和低数值阻尼的优点,且计算工作量大大小于协调单元法,有利于推广应用于对流扩散方程的数值求解.
심조일충고정도적공간단원삽치모식시수치구해삼유대류문제적관건.재전인연구적기출상,탐토료일충임의공간륙면체적의협조단원,보증절점상적물리량함수급기일계도수련속.산례표명,해방법구유량호적계산은정성화저수치조니적우점,차계산공작량대대소우협조단원법,유리우추엄응용우대류확산방정적수치구해.
There are a fundamental difficulty in solving equations due mainly toadvective transport. Numerical problems associated with advectivedomainted transport include spurious oscillation, numerical dispersion,peak clipping, and grid oriention. It is well known and has been welldemonstrated that the classical first order scheme would generateexcessive numerical dispersion while higher order scheme have beenpresented to prevent numerical dispersion without the problems ofspurious oscillation around the shock. However,the key of numerical solution of three-dimensional advective problem issearching for a high-precision interpolating function, which keep thenumerical stability and low damping. For the pure 3D advection problem,solutions are found by the method of characteristics. The solutionalgorithm involves tracing the characteristic lines backwards in timefrom a vortex of an element of an interior point. Based on the reference ［9］, aadvanced quasi-consistence hexahedral element method forthree-dimensional advective problem is developed in this paper. The flowdomain is discretized into arbitrary hexahedral elements. A third-orderpolynomial based on three-dimensional cartesian coordinates (x, y, z) isadopted as the element interpolating function to ensure that the variablefunctions and their first derivatives over the entire domain arecontinuous. The function is different from that of thereference ［9］, avoid solving the linear equations which is 6464order at every time step, and can only spend 1/50 computer time for thealgorithm on reference ［9］. The verification of the algorithm areperformed using a Guass-distributed concentration ball and astock wave at steady flow in an open channel, respectively. Thecomparison with an analytical problem solution show that the precisionand the stability of this algorithm is as good as that of the reference［9］, better than that of the linear interpolating function method.