Construction of explicit and implicit symmetric TVD schemes and their applications. [Total Variation Diminishing for fluid dynamics computation]
Construction of explicit and implicit symmetric TVD schemes and their applications. [Total Variation Diminishing for fluid dynamics computation]
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DOI：
10.1016/0021-9991(87)90049-0
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发表时间：
1987-01
期刊：
影响因子：
--
通讯作者：
H. C. Yee
中科院分区：
文献类型：
--
作者：
H. C. Yee
对单参数二阶显式和隐式总变差递减（TVD）格式族进行了重新表述，使其包含了一组更简单、更广泛的限制器。由此产生的计划可以被看作是一个对称的算法与各种数值耗散项，是专为弱解的双曲型问题。这是Roe和Davis最近的工作的推广到比Lax-Wendroff更广泛的一类对称方案。这类格式的主要性质是它们可以是隐式的，并且当寻求稳态计算时，数值解与时间步长无关。二维非定常和定常翼型计算的数值实验表明，所提出的对称TVD格式是相当强大和准确的。
A one-parameter family of second-order explicit and implicit total variation diminishing (TVD) schemes is reformulated so that a simplier and wider group of limiters is included. The resulting scheme can be viewed as a symmetrical algorithm with a variety of numerical dissipation terms that are designed for weak solutions of hyperbolic problems. This is a generalization of recent works of Roe and Davis to a wider class of symmetric schemes other than Lax-Wendroff. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. Numerical experiments with two-dimensional unsteady and steady-state air-foil calculations show that the proposed symmetric TVD schemes are quite robust and accurate.