论文标题
订单自适应的紧凑型近似泰勒方法，用于保护法。
An order-adaptive compact approximation Taylor method for systems of conservation laws
论文作者
论文摘要
我们提出了一个新的高阶冲击捕捉有限差异数值方法的家族，用于保护法律系统。这些方法称为自适应紧凑型近似泰勒（ACAT）方案，使用中心$（2p + 1）$ - 点模板，其中$ p $可能会根据$ \ {1、2，\ dots，p \} $在模板中的新型平滑度指示器中使用。这些方法基于强大的一阶方案和紧凑的近似泰勒（CAT）订单$ 2P $ - 订单的方法，$ p = 1,2，\ dots，p $，以便它们在不连续性附近准确地准确，并且在平稳地区具有$ 2p $的订单$ 2p $，其中$（2p +1）$（2p +1）$（2p +1）是最大的典范的大小。 \ cite {cp2019}中介绍的猫方法是延伸到非线性问题的延伸，cauchy-kovelesky（ck）程序是根据\ cite {zbm2017}中提出的较高的综合范围划分的策略来规避的cauchy-kovelesky（ck）程序的范围，该过程范围范围范围范围，该策略均可在\ cite {zbm2017}中进行综合范围。 时间。给出了1D和2D平衡法系统的ACAT方法的表达，并在许多测试用例中测试了几种线性和非线性保护定律系统的测试案例，包括气体动力学的Euler方程。
We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered $(2p + 1)$-point stencils, where $p$ may take values in $\{1, 2, \dots, P\}$ according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order $2p$-order, $p=1,2,\dots, P$ so that they are first order accurate near discontinuities and have order $2p$ in smooth regions, where $(2p +1)$ is the size of the biggest stencil in which large gradients are not detected. CAT methods, introduced in \cite{CP2019}, are an extension to nonlinear problems of the Lax-Wendroff methods in which the Cauchy-Kovalesky (CK) procedure is circumvented following the strategy introduced in \cite{ZBM2017} that allows one to compute time derivatives in a recursive way using high-order centered differentiation formulas combined with Taylor expansions in time. The expression of ACAT methods for 1D and 2D systems of balance laws are given and the performance is tested in a number of test cases for several linear and nonlinear systems of conservation laws, including Euler equations for gas dynamics.
