This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enable applications of fast algebraic solvers. We present details for the second order accurate parametric scheme based on the finite volume method including simple variants of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) approximations. We present numerical experiments for representative linear and nonlinear problems.

翻译：本文研究利用一种新型紧凑隐式时间离散格式求解二维守恒律的数值方法，该格式支持快速代数求解器的应用。我们详细介绍了基于有限体积法的二阶精度参数化格式，包括ENO（基本无振荡）和WENO（加权基本无振荡）近似方法的简化变体。针对典型线性和非线性问题，我们给出了数值实验的结果。