Parallel adaptive mesh refinement for incompressible flow problems

We present an algorithm for the solution of the incompressible Navier- Stokes equations combined with local refinement of the mesh based on an error estimation. Our solution strategy is based on well-established CFD techniques and has been designed to be efficient and scalable in a parallel environment. This has proved to be specially challenging for the mesh refinement, for which we propose an algorithm designed to use as little non-local information as possible. We complement the discussion with a numerical example.Postprint (published version

Introducing CFD Numerical Analysis in Fluid Dynamics to Junior Engineering Students

Western Illinois University engineering faculty introduce ANSYS workbench during Fluid Dynamics, a junior level core-engineering course in many engineering programs. Traditionally, advanced analytical software is not introduced until the senior year or in graduate courses. However, since the methods of teaching engineering have evolved dramatically toward using advanced technological tools and software, the use of ANSYS workbench software in the junior year is now quite natural. Using advanced numerical software provides students with better understanding and visualization of a flow field. The current generation of students is accustomed to watching videos and animations to grasp a concept or an idea. The animations, contours and figures generated using a CFD numerical analysis program provide X university\u27s engineering students with a greater understanding of flow behavior in all but the simplest dynamic fluid problems. As in most programs, physical laboratory experiments are conducted in the fluid dynamics class. Then the students model the experiments using CFD simulations. Consequently, both the experimental and numerical results are able to be compared and validated. The decision to use advanced CFD software in the fluid dynamics class has produced a positive impact on the student\u27s overall knowledge of fluid mechanics. The students are excited to use state of the art analysis techniques and demonstrate greater enthusiasm in class

Course4a-Heat Transfer

INTRODUCTION TO COMPUTATIONAL METHOD

A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations

A finite element method to solve the bidimensional Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotical simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These aretherefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element discretization, based on a piecewise constant approximation of the pressure, is proposed and analyzed. Numerical experiments which consist in fluid flow simulations within a constricted pipe are provided. Comparisons with Navier-Stokes simulations allow to evaluate the performance of prediction of the finite element method, and of the model itself

Mathematical modeling of coolant flow in discontinuous drilling processes with temperature coupling

Nickel-based alloys, like Inconel 718, are widely used in industrial applications due to their high-temperature strength and high toughness. However, machining such alloys is a challenging task because of high thermal loads at the cutting edge and thus extensive tool wear is expected. Consequently, the development of new process strategies is needed. We will consider the discontinuous drilling process with coolant. The main idea is to interrupt the drilling process in order to let the coolant to flow around the cutting edge and to reduce thermal loads. Since measurements inside the borehole are (nearly) impossible, simulations are a key tool to analyze and understand the proposed process. In this paper, a 3D fluid flow simulation model with Q2P1 Finite Elements in combination with the Fictitious Boundary Method is presented to simulate the coolant flow around the drill inside the borehole. The underlying equations are transformed into a rotational frame of reference overcoming the challenges of mesh design for high rotational domains inside the fluid domain. Special treatment of Coriolis forces is developed, that modifies the ‘Pressure Poisson’ Problem in the projection step improving the solver for high angular velocities. To further take high velocities into account, a two-scale artificial diffusion technique is introduced to stabilize the simulation. Finally, Q1 Finite Elements are used to simulate the heating and cooling processes in both the tool and the coolant during the complete discontinuous drilling process. The simulation is split into a ‘contact’ and a ‘no contact’ phase and a coupling strategy between these phases is developed. FBM is utilized to switch between the two configurations, thus only one unified grid for both configurations is needed. The results are used to gain insight into the discontinuous drilling process and to optimize the process design

Fast solvers and efficient numerical cfd techniques for dynamic porous media problems

We present a fully implicit, monolithic finite element solution scheme to efficiently solve the governing set of differential algebraic equations of incompressible poroelastodynamics. Thereby, we proceed from a two-dimensional, biphasic, saturated porous medium model with intrinsically coupled and incompressible solid and fluid constituents. Our approach, motivated by well-accepted CFD techniques and originally developed for the efficient simulation of incompressible flow problems, is characterized by the following aspects: (1) a special treatment of the algebraically coupled volume balance equation leading to a reduced form of the boundary conditions; (2) usage of a higher-order accurate mixed LBB-stable finite element pair with piecewise discontinuous pressure for the spatial discretization; (3) application of the fully implicit 2nd-order Crank-Nicolson scheme for the time discretization; (4) use of a special fast multigrid solver for the resulting discrete linear equation system. For the purpose of validation and to expose the merits and benefits of our new solution strategy in comparison to other established approaches, canonical one- and two-dimensional wave propagation problems are solved. Finally, a large-scale, dynamic soil-structure interaction problem serves to reveal the efficiency of the special multigrid solver in combination with the chosen finite element discretization

Using Python to Solve the Navier-Stokes Equations - Applications in the Preconditioned Iterative Methods

This article describes a new numerical solver for the Navier-Stokes equations. The proposed solver is written in Python which is a newly developed language. The Python packages are built to solve the Navier-Stokes equations with existing libraries. We have created discretized coefficient matrices from systems of the Navier-Stokes equations by the finite difference method. In addition we focus on the preconditioned Krylov subspace iterative methods in the linearized systems. Numerical results of performances for the Preconditioned iterative methods are demonstrated. The comparison between Python and Matlab is discussed at the end of the paper

A CutFEM method for two-phase flow problems

In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising advection and the pressure-velocity coupling and, on the other hand, stabilising the cut region. The accuracy of the algorithm is enhanced by the development of extended fictitious domains to guarantee a well defined velocity from previous time steps in the current geometry. Finally, the robustness of the moving-interface algorithm is further improved by the introduction of a curvature smoothing technique that reduces spurious velocities. The algorithm is shown to perform remarkably well for low capillary number flows, and is a first step towards flexible and robust CutFEM algorithms for the simulation of microfluidic devices

Adaptive Time Stepping for Transient Network Flow Simulation in Rocket Propulsion Systems

Fluid and thermal transients found in rocket propulsion systems such as propellant feedline system is a complex process involving fast phases followed by slow phases. Therefore their time accurate computation requires use of short time step initially followed by the use of much larger time step. Yet there are instances that involve fast-slow-fast phases. In this paper, we present a feedback control based adaptive time stepping algorithm, and discuss its use in network flow simulation of fluid and thermal transients. The time step is automatically controlled during the simulation by monitoring changes in certain key variables and by feedback. In order to demonstrate the viability of time adaptivity for engineering problems, we applied it to simulate water hammer and cryogenic chill down in pipelines. Our comparison and validation demonstrate the accuracy and efficiency of this adaptive strategy