Different from the spatial semi-discrete WENO schemes based on RK method in time, this paper presents a fully-discrete scheme with consistent high order in time and space based on solution formula method. Analyzing the error composition of the framework, we obtain two core steps of discretization for constructing high-order schemes: initial value reconstruction and flux reconstruction. During the reconstruction, we apply the Newton interpolation with WENO thought and newly designed limiters to maintain robustness. Since the new method uses WENO reconstruction on fully-discrete framework, we name the new scheme as Full-WENO. With characteristics projection and Strang split technique, we extend the method to multi-dimensional Euler equations under curvilinear coordinates. The new scheme has following advantages: (1) One-step to consistent high order in time and space with excellent shock-capturing capacity; (2) Achieving exact solution in linear cases and performing better in nonlinear cases when CFL→1, and even can be stably implemented under CFL=1; (3) High resolution, especially for long-time evolution problems; (3) High efficiency, Full-WENO is s times faster than classical WENO with s-stage RK method under same computing condition; (4) Entropy condition automatically satisfied without additional artificial numerical viscidity. Numerical experiments contain tests of accuracy order, linear and nonlinear scalar equation, 1D and 2D Euler equations, efficiency, and sonic point. All of these verify the new scheme is equipped with the merits of high order, high resolution, and high efficiency.

与时间上基于RK方法的空间半离散WENO格式不同，本文提出一种基于求解公式方法的时空高阶一致的全离散格式。通过分析该框架的误差构成，我们得到了构造高阶格式的离散化的两个核心步骤：初值重构和通量重构。在重建过程中，我们应用牛顿插值和WENO思想以及新设计的限制器来保持鲁棒性。由于新方法在全离散框架上使用WENO重构，因此我们将新方案命名为Full-WENO。利用特征投影和Strang分裂技术，我们将该方法扩展到曲线坐标下的多维欧拉方程。新方案具有以下优点：（1）一步实现时间和空间上的高阶一致，具有优异的冲击捕捉能力； (2) 当CFL→1时，在线性情况下能够实现精确解，在非线性情况下表现更好，甚至在CFL=1下也能稳定实现； （3）高分辨率，特别是对于长时间演化问题； （3）效率高，相同计算条件下Full-WENO比经典WENO加s级RK方法快s倍； (4)自动满足熵条件，无需额外的人工数值粘度。数值实验包括精度阶次、线性和非线性标量方程、一维和二维欧拉方程、效率和声波点的测试。这些都验证了新方案具有高阶、高分辨率、高效率的优点。