Lennart Schneiders

An accurate moving boundary formulation in cut-cell methods

A cut-cell method for Cartesian meshes to simulate viscous compressible flows with moving boundaries is presented. We focus on eliminating unphysical oscillations occurring in Cartesian grid methods extended to moving-boundary problems. In these methods, cells either lie completely in the fluid or solid region or are intersected by the boundary. For the latter cells, the time dependent volume fraction lying in the fluid region can be so small that explicit time-integration schemes become unstable and a special treatment of these cells is necessary. When the boundary moves, a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level. This causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme. This temporally discontinuous alteration is shown to act like an unphysical source term, which deteriorates the numerical solution, i.e., it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary. We develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut-cell method which avoids these discontinuities. Results for canonical two- and three-dimensional test cases evidence the accuracy and robustness of the newly developed scheme.

An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows

A Cartesian cut-cell method for viscous flows interacting with freely moving boundaries is presented. The method enables a sharp resolution of the embedded boundaries and strictly conserves mass, momentum, and energy. A new explicit Runge-Kutta scheme (PC-RK) is introduced by which the overall computational time is reduced by a factor of up to 2.5. The new scheme is a predictor-corrector type reformulation of a popular class of Runge-Kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy. The structural motion is computed by an implicit scheme with good stability properties due to a strong-coupling strategy and the conservative discretization of the flow solver at the material interfaces. A new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted Taylor-series approach solved via singular-value decomposition. The efficiency and the accuracy of the new method are demonstrated for several three-dimensional cases of laminar and turbulent particulate flow. It is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid-solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed. The results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes. An efficient Cartesian cut-cell method for freely moving solid boundaries is presented.The new predictor-corrector Runge-Kutta scheme (PC-RK) enables simulation speedups of up to 2.5.Mass, momentum, and energy are strictly conserved at the sharply resolved solid-fluid interfaces.The method exhibits very good stability and accuracy properties even for large displacements of the boundaries.Spurious force oscillations inherent to this class of methods are suppressed.

Sharp resolution of complex moving geometries using a multi-cut-cell viscous flow solver

In many engineering problems the sharp resolution of the flow field near irregularly shaped boundaries is essential, e.g., for the flow in complex geometries such as internal combustion engines or for particulate flows with irregular particle shapes or inter-particle and wall-particle collisions. Especially when moving boundaries are involved, immersed boundary methods have been increasingly used for the simulation of such flows during the past decades. Among the different immersed boundary variants the cut-cell method is the only strictly mass-conserving approach and is capable of providing a sharp resolution of arbitrarily complex boundary configurations. In cut-cell methods, Cartesian cells that are intersected by the boundary surfaces are reshaped to retain only the fluid fraction of the original cell volume. However, computing the intersections of Cartesian cells with complex or non-smooth boundaries is tedious and difficult to be realized in a generic and robust fashion. In this study, a new multi-cut-cell method is presented in which complex intersections of a single Cartesian cell with multiple surfaces are handled by a generic and conceptionally simple procedure. In this strict finite-volume approach, an accurate representation of different boundary conditions within a single cell is realized. Sharp features of the boundaries and independently moving objects are tracked by a multiple-level-set formulation which preserves non-smooth regions of the boundary. The accuracy of the new method is demonstrated for several three-dimensional flow configurations involving moving boundaries, such as the turbulent flow field in a realistic internal combustion engine and colliding particles.

Validation of Particle-Laden Large-Eddy Simulation Using HPC Systems

In this contribution, results of a direct particle-fluid simulation (DPFS) are compared with direct numerical simulations and large-eddy simulations (LES) using a popular Euler-Lagrange method (ELM). DPFS facilitates the computation of particulate turbulent flow with particle sizes on the order of the smallest flow scales, which requires advanced numerical methods and parallelization strategies accompanied by considerable computing resources. After recapitulating methods required for DPFS, a setup is proposed where DPFS is used as a benchmark for direct numerical simulations and LES. Therefore, a modified implicit LES scheme is proposed, which shows convincing statistics in comparison to a direct numerical simulation of a single phase flow. Preliminary results of particle-laden flow show good agreement of the LES and the DPFS findings. Further benchmark cases for an appreciable range of parameters are required to draw a rigorous conclusion of the accuracy of the ELM.

A robust cut-cell method for fluid-structure interaction on adaptive meshes

A new cut-cell method to simulate the interaction of a viscous fluid with rigid boundaries is presented. The method is based on a strictly conservative Cartesian cut-cell scheme and accounts accurately for the fluid forces exerted on the solid boundaries. The boundaries are represented using a signed-distance function by which one or multiple immersed bodies can be tracked efficiently. In particular, the new method aims at suppressing spurious force oscillations which are typically encountered in sharp interface Cartesian methods applied to moving boundary problems and may deteriorate the accuracy of the fluid-structure momentum exchange. These unphysical oscillations are traced back to the frequent generation and cancellation of grid cells due to the boundary motion. The new discretization scheme is applied in cells close to the solid interfaces which eliminates these numerical discontinuities. Results for twoand three-dimensional flows involving moving boundaries demonstrate the accuracy and the robustness of the novel method.