The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of finite volume Eulerian-Lagrangian methods for the solution of non-linear problems in two space dimensions on unstructured triangular meshes. The proposed approach belongs to the class of predictor-corrector procedures where the numerical fluxes are reconstructed using the method of characteristics, while an Eulerian method is used to discretize the conservation equation in a finite volume framework. The scheme is accurate, conservative and it combines advantages of the modified method of characteristics to accurately solve the non-linear conservation laws with a finite volume method to discretize the equations. The proposed Finite Volume Characteristics (FVC) scheme is also non-oscillatory and avoids the need to solve a Riemann problem. Several test examples will be presented for the shallow water equations. The results will be compared to those obtained with the Roe.

翻译：流体迁移和流体动力学问题通常采取保护法双曲系统的形式。在这项工作中,我们将提出解决这些进化方程式的有限体积方法新办法。这是用数量有限的欧莱安-拉格朗加法解决非线性问题的方法在非结构化三角模头两个空间层面解决非线性问题的一个组合。提议的办法属于预测者-校正程序一类,即利用特性方法重建数字通量,同时使用欧莱安法将保护方程式分解成数量有限的体积框架。这个办法准确、保守,它结合了经修改的特性方法的优势,用数量有限的方法准确解决非线性保护法,将方程式分解。拟议的非线性体积特征学(FVC)办法也是非系统性的,避免了解决里曼问题的必要。将用几个试验例子来说明浅水方程式。其结果将与与Roe比较。