A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, $\mathrm{M}\approx 0.1$, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to a genuinely incompressible formulation. Our contributions to the state-of-the-art are twofold: Firstly, we present a high-performance discontinuous Galerkin solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures. The performance results presented in this work focus on the node-level performance and our results suggest that there is great potential for further performance improvements for current state-of-the-art discontinuous Galerkin implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows

Dealiasing techniques for high-order spectral element methods on regular and irregular grids

High-order methods are becoming increasingly attractive in both academia and industry, especially in the context of computational fluid dynamics. However, before they can be more widely adopted, issues such as lack of robustness in terms of numerical stability need to be addressed, particularly when treating industrial-type problems where challenging geometries and a wide range of physical scales, typically due to high Reynolds numbers, need to be taken into account. One source of instability is aliasing effects which arise from the nonlinearity of the underlying problem. In this work we detail two dealiasing strategies based on the concept of consistent integration. The first uses a localised approach, which is useful when the nonlinearities only arise in parts of the problem. The second is based on the more traditional approach of using a higher quadrature. The main goal of both dealiasing techniques is to improve the robustness of high order spectral element methods, thereby reducing aliasing-driven instabilities. We demonstrate how these two strategies can be effectively applied to both continuous and discontinuous discretisations, where, in the latter, both volumetric and interface approximations must be considered. We show the key features of each dealiasing technique applied to the scalar conservation law with numerical examples and we highlight the main differences in terms of implementation between continuous and discontinuous spatial discretisations

IMAGE CHARGE SOLVATION MODEL (ICSM) FOR SIMULATING BIOMOLECULES AND KCSA ION-CHANNELS

We present an order N method for calculating electrostatic interactions that has been integrated into the molecular dynamics portion of the TINKER Molecular Modeling package. This method, termed the Image-Charge Solvation Model (ICSM), and introduced previously by Dr. Lin et al. (1) in 2009, is a hybrid electrostatic approach that combines the strengths of both explicit and implicit representations of the solvent. In this model, a multiple-image method is used to calculate reaction fields due to the implicit solvent while the Fast Multipole Method (FMM) is used to calculate the Coulomb interactions for all charges, including the charges in the explicit solvent part. The integrated package is validated through simulations of liquid water. The results are compared with those obtained by the Particle Mesh Ewald (PME) method that is built in the TINKER package. Timing performance of TINKER with the integrated ICSM is benchmarked on bulk water as a function of the size of the system. In particular, timing analysis results show that the ICSM outperforms the PME for sufficiently large systems with the break-even point at around 30,000 particles in the simulated system. To demonstrate the capability of the package on large macromolecules, the model is used to simulate the potassium channel KcsA

Advances in Modeling of Fluid Dynamics

This book contains twelve chapters detailing significant advances and applications in fluid dynamics modeling with focus on biomedical, bioengineering, chemical, civil and environmental engineering, aeronautics, astronautics, and automotive. We hope this book can be a useful resource to scientists and engineers who are interested in fundamentals and applications of fluid dynamics

TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD

Derivation of an unambiguous incompressible form of the lattice Boltzmann equation is pursued in this dissertation. Further, parallelized implementation in developing application areas is researched. In order to achieve a unique incompressible form which clarifies the algorithm implementation, appropriate ansatzes are utilized. Through the Chapman-Enskog expansion, the exact incompressible Navier-Stokes equations are recovered. In initial studies, fundamental 2D and 3D canonical simulations are used to evaluate the validity and application, and test the required boundary condition modifications. Several unique advantages over the standard equation and alternative forms found in literature are found, including faster convergence, greater stability, and higher fidelity for relevant flows. Direct numerical simulation and large eddy simulation of transitional and chaotic flows are one application area explored with the derived incompressible form. A multiple relaxation time derivation is performed and implemented in a 2D cavity (direct simulation) and a 3D cavity (large eddy simulation). The Kolmogorov length scale, a function of Reynolds number, determines grid resolution in the 2D case. Comparison is made to the extensive literature on laminar flows and the Hopf bifurcation, and final transition to chaos is predicted. Steady and statistical properties in all cases are in good agreement with literature. In the 3D case the relatively new Vreman subgrid model provides eddy viscosity modeling. By comparing the center plane to the direct numerical simulation case, both steady and unsteady flows are found to be in good agreement, with a coarse grid, including prediction of the Hopf bifurcation. Multiphysics pore scale flow is the other main application researched here. In order to provide the substrate geometry, a straightforward algorithm is developed to generate random blockages producing realistic porosities and passages. Combined with advection-diffusion equations for conjugate heat transfer and soot particle transport, critical diesel particulate filtration phenomena are simulated. To introduce additional fidelity, a model is added which accounts for deposition caused by a variety of molecular and atomic forces. Detailed conclusions are presented to lay the groundwork for future extensions and improvements. Predominantly, higher lattice velocity large eddy simulation, improved parallelization, and filter regeneration