This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of threedimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively-based on upscaled parameters such as surface area, solid volume, and effective reaction rate-and qualitatively-based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.

This paper is devoted to the design of Vortex-In-Cell (VIC) methods for the direct numerical simulations of wallbounded flows. A first method using body-fitted grid is presented in the particular case of a cylinder wake. This method, which has been used in [Phys. Fluids 14(6) (2002) 2021] to investigate the effect on the wake topology of cylinder rotations, is an extension of the VIC method presented in [J. Comput. Phys. 175 (2002) 702] for periodic geometries. Features of the method that are specific to wall-bounded geometries -interpolation operators, field calculations and vorticity flux formulas to enforce no-slip boundary conditions -are described in details. The accuracy of the method in the calculation of the body forces is investigated by comparisons with experiments and benchmark calculations. A second class of methods is in the spirit of the immersed boundary methods. The paper in particular shows that the noslip conditions are very naturally handled by the vorticity flux formulas, independently of the relative locations of the particles and the body. Numerical experiments on the test-case of a ring impinging on a cylinder suggest that the method is second-order accurate.

The development of a three-dimensional viscous incompressible flow generated behind an infinitely long circular cylinder, impulsively started into rectilinear motion and rotationally oscillating, is studied computationally. The numerical scheme, an hybrid vortex method, is used to integrate the velocity-vorticity formulation of the Navier-Stokes equations. The Reynolds number considered is Re ¢ ¡ ¤ £ ¥ £ , which is moderate though beyond the critical values Re¦ § © £ and Re ¦ § £ for which the flow becomes spontaneously three-dimensional. The numerical method is explained and its main points are developped. This scheme is then applied to solve a few two-dimensional problems, both in order to validate the method and to compute a nominal twodimensional flow, required to measure the impact of three-dimensionality. The three-dimensional flow past a steady cylinder is also compared to benchmark simulations. Once the flow has become fully three-dimensional, beyond transient regime and saturation of instabilities, the cylinder begins a rotary oscillation around its axis. Two kinds of rotations are considered, either at constant amplitude and several frequencies, or at constant frequency and various amplitudes. When amplitude and frequency are high enough, the whole flow comes back to its two-dimensional state. This result gives a justification for two-dimensional computations present in the literature related to rotating cylinders. For the first super-harmonic frequency of the flow, a parametric study is realized in order to get the impact of the amplitude on the topology of the flow. A bifurcation is clearly identified. Eventually, the mechanisms involved in the return to a two-dimensional state are explained : the interaction between transverse instabilities and von Kármán alleys is quantified by means of a correlation analysis.

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