Session GB: Computational Fluid Dynamics II

An Adaptive Wavelet Shock Capturing Scheme for Compressible Inert and Reactive Flows

Most TVD schemes make use of artificial viscosity to reduce oscillations when solving hyperbolic conservation equations. In order to minimize the numerical dissipation introduced by artificial viscosity, high order TVD, WENO and MUSCL type schemes have been developed which require multistep finite volume calculations. Although there is a significant improvement in discontinuity steepness, it ultimately results in an increase of the overall computational cost of the numerical scheme. The current research seeks to develop a method that optimizes the computational cost by combining an inexpensive shock capturing viscosity scheme with the advantages that a dynamically adaptive wavelet-collocation method allows. A technique has been developed to reduce oscillations near a shock or discontinuity by explicitly adding localized dissipation terms in discontinuous regions while having zero dissipation elsewhere. In order to minimize the amount of dissipation introduced into the solution, which is especially important in reacting flows, the method only applies the viscosity proportional to the wavelet coefficients that are above a given threshold parameter. The main advantage of this technique is its generality and lack of dependence on the initial conditions as well as its simplicity and lower computational cost. Single and multi-dimensional demonstrations including inert and reactive flows are given and discussed.   

Dynamic Phase Boundaries for Compressible Fluids

We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. The transition is modeled as a tracked jump discontinuity; the mass, momentum, and energy conservation laws across the phase boundary are solved as a generalized Riemann problem; the phase transition rate is associated with the deviation from phase equilibrium by the kinetic theory. The emphasis here is on the coupling of the phase transition process to acoustic waves, which is required for the study of cavitation induced by strong rarefaction waves. The robustness of the proposed algorithm is verified by application to various physical regimes.   

A One-Dimensiontal Conservative Method to Track Contact Discontinuities in a Compressible Medium

We present a one-dimensional algorithm to track an interface between two compressible media. The method can readily be extended to multiple dimensions. The moving interface cuts out time-varying control volumes and a consistent finite-volume discretization is derived by applying the divergence theorem in space-time. The method is fully conservative, even at the discontinuity, and the truncation error is expected to be first-order at the boundary between the two fluids, which is one order higher than conventional methods. Classical benchmark results and convergence studies are presented.   

Continuum-microscopic computation of complex fluid flow

A method to compute the continuum flows of a fluid defined through its micrscopic behavior is presented. Adaptive mesh refinement is employed on the continuum level to dynamically locate areas where the continuum constitutive laws no longer hold. Areas so identified are sampled at a microscopic level in accordance with some microscopic model (e.g. Kelvin, Zener, Burgers for viscoelastic flows) which features spatially varying properties. A hierarchical microscopic simulation is carried out in order to computationally identify statistical moments entering into the continuum level consitutive law. Dynamics from a finer level of microscopic simulation are analyzed through principal orthogonal decomposition and higher-order tensor decompositions in order to identify modes that are representable on a coarser level. Thermal background is captured through a multi-level heat equation. Applications especially related to bio-fluids problems are presented.   

An ALE-Based Unstructured-Grid Solver for Fluid-Structure Interaction.

An implicit structural dynamics solver is coupled with a fluid dynamics solver through the Arbitrary Lagrangian-Eulerian (ALE) method on an unstructured mesh framework to study fluid-structure interaction (FSI) phenomena. The fluid and structure solutions are updated in an iterative manner with a dynamic mesh algorithm. This study aims to improve the efficiency and accuracy of the coupled FSI solver. With the adoption of the dynamic mesh algorithm, the efficiency of unsteady flow simulation is improved and large structural deformation can be handled without excessive distortion of the meshes near the moving structure. The FSI solver is applied to simulate the vortex induced vibrations of an elastic plate under different initial conditions. Both cases with a rigid plate and an elastic plate are investigated for comparison. The results agree well with existing numerical and experimental data. It is observed that the vortex shedding patterns and frequencies for both cases are different and the solution for an elastic plate varies with the initial deflection of the plate.   

Solving turbulent wall flow in 2D using volume-penalization on a Fourier basis

The volume-penalization method allows in principal the use of fast Fourier pseudospectral techniques to simulate turbulent wall flows. Convergence checks with respect to the spacial resolution, time stepping and the penalization strength are presented where a challenging dipole-wall collision simulation serves as a benchmark (obtained by a high-resolution 2D Chebyshev scheme). It is found that Gibbs oscillations have a minor effect on the flow dynamics, which allows post-processing techniques to recover higher order accuracy. The procedure is much cheaper than the more classical Chebyshev Navier-Stokes solvers. Therefore the potential is further examined by considering the statistical properties of fully developed 2D turbulence in bounded domains with Reynolds numbers substantially larger than previously possible.   

Development of Unstructured MARS: Multi-interface Advection {\&} Reconstruction Solver

The MARS was originally developed as a direct numerical simulation (DNS) for multiphase flows (MF) including large free-surface deformation on a staggered structured grid system. The usage of an unstructured grid in the computational fluid dynamics (CFD) areas is now to be popular manner for handling the complex geometry of the computational domain. However, majority of unstructured CFD codes is focused on single phase flows and/or simple two-phase flows. In the present study, we are developing an unstructured DNS-MF solver based on the MARS. We choose the collocated grid system for all variables to fit the unstructured grid system and then the Poisson solver for the pressure equation derived by the fractional-step algorithm is modified by the Rhie-Chow method. We carry out the comparison study of a `Dam breaking problem' between the staggered MARS and collocated MARS in order to investigate the effect of the grid systems on the free surface tracking. This computation requires a high accuracy, so that we use the structured grid system in this case. Finally, we will show the difference between them, and will discuss the manner of the surface tracking.   

Particle-Based Methods for Fluid Dynamics Simulation.

Meshless finite-mass particle-based methods have showed attractive numerical features and potential to serve as computational platform for multiphase fluid dynamics problems with complex topological patterns and interfacial breakup. At their foundation, the particle methods are built on the Lagrangian concept of fluid tracer which, intuitively, is highly physical. Using the tracer to represent a real fluid mass is however problematic, as complex flow involves shearing and stretching, where fluid-element deformation and eventually mixing/dissolution are inherently incompatible with the finite-mass undeformable particle treatment. In this paper we examine the applicability of two particle methods (SPH, MPS) by relating their solution accuracy to the particle residence time scale in selected test problems in confined and free-surface geometry. We propose a novel algorithm of a dynamically-corrected particle method to effectively increase the solution accuracy in long transients, and discuss preliminary results of the method implementation and testing.   

Vortex-induced Oscillations and Heat Transfer on a Cylinder in Accelerated Flow

We propose a new method for solving aeroelasticity problems that combines numerical treatment of the Navier-Stokes equations with analytical solution of the dynamics equations on each time step. The numerical-analytical algorithm developed enables a systematic study of otherwise computationally-expensive fluid-structure interaction problems that span over a large time interval. Of both theoretical and practical interest is the effect of flow acceleration on aeroelastic oscillations and heat transfer at low Reynolds numbers. The present numerical work predicts several oscillation modes in a lower range of a dimensionless acceleration parameter $A_{F}$, whereas the oscillation modes diminish as $A_{F}$ increases. The paper also discusses interesting heat transfer behaviour predicted to occur at low $A_{F }$ in the resonant lock-in regime.   

A Cartesian Mesh Method for Fluid-Structure Interaction

Flow-structure interaction with finite solid deformation, of the kind common in biological systems, is well known to be challenging to simulate. There are fundamental differences in the material properties that make coupling difficult at the interface, whose position is not generally known a priori. The characteristics of solids and fluids are such that fluids are more naturally represented by an Eulerian formulation, and solids, because the referential state is important, are more naturally represented by a Lagrangian formulation. We have developed a Cartesian mesh method to simulate the combined system that preserves the attractive aspects of each formulation. The solid motion is tracked as in any Lagrangian formulation, while the momentum equations for both the solid and fluid are solved on a uniform Cartesian mesh. The solid stresses are computed on an unstructured mesh by using a finite element discretization and are distributed to the Cartesian mesh with conservative interpolation. Both fluids and solids are incompressible, as appropriate for biological systems. This condition is enforced via constraints. No artificial bulk modulus is employed. Convergence results are presented, as well as example simulation results for an advected deformable body, a very flexible leaflet, and a swimming jellyfish. Research supported by DOE.