An implicit Cartesian cut-cell method for incompressible viscous flows with complex geometries

Highlights

• A 3D cut-cell method is presented for incompressible viscous flows with complex geometries.

• The “small cut-cell” problem is addressed by implicit time integration to avoid stability issues.

• A conservative and consistent mass and momentum flux computation is used for finite volume method.

• The method is validated for flow over cylinder, airfoil, sphere, pipe, and complex heart sculpture.

• Good agreement with experiment, and other body-fitted, immersed boundary/interface, and cut-cell methods.

Abstract

A versatile conservative three-dimensional Cartesian cut-cell method for simulation of incompressible viscous flows over complex geometries is presented in this paper. The present method is based on the finite volume method on a non-uniform staggered grid together with a consistent mass and momentum flux computation. Contrary to the commonly cut-cell methods, an implicit time integration scheme is employed in the present method, which avoids numerical instability without any additional small cut-cell treatment. Strict conservation of the mass and momentum for both fluid and cut cells is enforced through the PISO algorithm for the pressure–velocity coupling. The versatility and robustness of the present cut-cell method are demonstrated by simulating various two- and three-dimensional canonical benchmarks (flow over a circular cylinder, airfoil, sphere, pipe, and heart sculpture) and the computed results agree well with previous experimental measurements and various numerical results obtained from the boundary-fitted, immersed boundary/interface, and other cut-cell methods, verifying the accuracy of the proposed method.