We present a k-exact reconstruction method, which can be incorporated into vertex-centered unstructured finite-volume flow solvers to maintain a high-order accurate solution in space. The scheme is combined with a fractional step strategy for the solution of the incompressible Navier-Stokes equations with a fully implicit discretization of a Poisson equation for the pressure correction. This also involves a novel approach for the flux discretization in the k-exact framework. It is shown, that a third order of accuracy can be maintained for the discretization of convective fluxes and a second order of accuracy for diffusive fluxes, even on highly distorted grids. The scheme is implemented into ThetaCOM, a turbulent heat release extension of DLR's TAU code in its combustion version, showing its applicability to be used in a full production flow solver. The improved properties of our approach in terms of performance and accuracy are demonstrated with several benchmarks cases in both two and three spatial dimensions.

我们提出了一种k精确重建方法，该方法可以结合到以顶点为中心的非结构化有限体积流求解器中，以保持空间中的高阶精确解。该方案与用于求解不可压缩 Navier-Stokes 方程的分步策略相结合，并使用 Poisson 方程的完全隐式离散化进行压力校正。这也涉及到k 中通量离散化的新方法- 精确的框架。结果表明，即使在高度扭曲的网格上，对流通量的离散化也可以保持三阶精度，扩散通量可以保持二阶精度。该方案在 ThetaCOM 中实施，这是 DLR 的 TAU 代码在其燃烧版本中的湍流热释放扩展，显示其适用于完整的生产流程求解器。我们的方法在性能和准确性方面的改进特性在两个和三个空间维度的几个基准案例中得到了证明。