A collocated finite-volume method for the incompressible Navier–Stokes problem is introduced. The method applies to general polyhedral grids and demonstrates higher than the first order of convergence. The velocity components and the pressure are approximated by piecewise-linear continuous and piecewise-constant fields, respectively. The method does not require artificial boundary conditions for pressure but requires stabilization term to suppress the error introduced by piecewise-constant pressure for convection-dominated problems. Both the momentum and continuity equations are approximated in a flux-conservative fashion, i.e., the conservation for both quantities is discretely exact. The attractive side of the method is a simple flux-based finite-volume construction of the scheme. Applicability of the method is demonstrated on several numerical tests using general polyhedral grids.

中文翻译：

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不可压缩的Navier-Stokes问题的并置有限体积方法

介绍了不可压缩的Navier-Stokes问题的并置有限体积方法。该方法适用于一般的多面体网格，并证明其高于一阶收敛性。速度分量和压力分别通过分段线性连续场和分段恒定场来近似。该方法不需要人工的压力边界条件，但需要稳定项来抑制由对流主导问题的分段恒定压力引入的误差。动量和连续性方程都是以磁通守恒的方式近似的，即，两个量的守恒都是离散精确的。该方法的吸引人之处是该方案基于简单的基于通量的有限体积构造。