High-order accurate kinetic energy and entropy preserving (KEEP) schemes in generalized curvilinear coordinates are proposed for stable and non-dissipative numerical simulations. The proposed schemes are developed on the basis of the physical relation that the fluxes in the Euler equations in generalized curvilinear coordinates can be derived by taking the inner product between the inviscid fluxes and the area vectors used for the coordinate transformation. To satisfy this physical relation discretely, this study proposes to interpret the area vector components as another individual variable and discretize the area vectors in the same way as other physical variables, such as the density and velocity. Consequently, the convective and pressure-related terms are discretized in a new split convective form, “quartic split form”, and quadratic split form, respectively. The high-order extension is straightforward, referring to the high-order formulations proposed for kinetic energy preserving schemes in a previous study. Numerical tests of vortex convection, inviscid Taylor-Green vortex, and turbulent boundary layer flow are conducted to assess the order of accuracy, the kinetic energy and entropy preservation property, and numerical robustness of the proposed KEEP schemes. The proposed high-order accurate KEEP schemes successfully perform long-time stable computations without numerical dissipation by preserving the total kinetic energy and total entropy well, even on a largely-distorted computational grid.

提出了广义曲线坐标中的高阶精确动能和熵保持（KEEP）方案，用于稳定和非耗散的数值模拟。所提出的方案是基于物理关系开发的，即广义曲线坐标下欧拉方程中的通量可以通过取无粘性通量与用于坐标变换的面积向量之间的内积来导出。为了离散地满足这种物理关系，本研究建议将面积向量分量解释为另一个单独的变量，并以与其他物理变量（例如密度和速度）相同的方式将面积向量离散化。因此，对流和压力相关项被离散为一种新的分裂对流形式，“四次分裂形式”，和二次分裂形式，分别。高阶扩展很简单，指的是先前研究中为动能保持方案提出的高阶公式。对涡流对流、无粘性泰勒-格林涡流和湍流边界层流进行了数值测试，以评估所提出的 KEEP 方案的精度、动能和熵保持特性以及数值鲁棒性。所提出的高阶精确 KEEP 方案通过很好地保留总动能和总熵，即使在严重失真的计算网格上也能成功地执行长时间稳定计算，而不会产生数值耗散。对涡流对流、无粘性泰勒-格林涡流和湍流边界层流进行了数值测试，以评估所提出的 KEEP 方案的精度、动能和熵保持特性以及数值鲁棒性。所提出的高阶精确 KEEP 方案通过很好地保留总动能和总熵，即使在严重失真的计算网格上也能成功地执行长时间稳定计算，而不会产生数值耗散。对涡流对流、无粘性泰勒-格林涡流和湍流边界层流进行了数值测试，以评估所提出的 KEEP 方案的精度、动能和熵保持特性以及数值鲁棒性。所提出的高阶精确 KEEP 方案通过很好地保留总动能和总熵，即使在严重失真的计算网格上也能成功地执行长时间稳定计算，而不会产生数值耗散。