Arbitrary Lagrangian-Eulerian form of flowfield dependent variation (ALE-FDV) method for moving boundary problems

Flowfield Dependent Variation (FDV) method is a mixed explicit-implicit numerical scheme that was originally developed to solve complex flow problems through the use of so-called implicitness parameters. These parameters determine the implicitness of FDV method by evaluating local gradients of physical flow parameters, hence vary across the computational domain. The method has been used successfully in solving wide range of flow problems. However it has only been applied to problems where the objects or obstacles are static relative to the flow. Since FDV method has been proved to be able to solve many complex flow problems, there is a need to extend FDV method into the application of moving boundary problems where an object experiences motion and deformation in the flow. With the main objective to develop a robust numerical scheme that is applicable for wide range of flow problems involving moving boundaries, in this study, FDV method was combined with a body interpolation technique called Arbitrary Lagrangian-Eulerian (ALE) method. The ALE method is a technique that combines Lagrangian and Eulerian descriptions of a continuum in one numerical scheme, which then enables a computational mesh to follow the moving structures in an arbitrary movement while the fluid is still seen in a Eulerian manner. The new scheme, which is named as ALE-FDV method, is formulated using finite volume method in order to give flexibility in dealing with complicated geometries and freedom of choice of either structured or unstructured mesh. The method is found to be conditionally stable because its stability is dependent on the FDV parameters. The formulation yields a sparse matrix that can be solved by using any iterative algorithm. Several benchmark stationary and moving body problems in one, two and three-dimensional inviscid and viscous flows have been selected to validate the method. Good agreement with available experimental and numerical results from the published literature has been obtained. This shows that the ALE-FDV has great potential for solving a wide range of complex flow problems involving moving bodies

A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains

A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier–Stokes equations on an unbounded staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation and incompressibility constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge–Kutta scheme for the convective term. A projection method that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rates, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. The accuracy and physical fidelity of solutions are verified through numerical simulations of vortex rings

A local mesh refinement approach for large-eddy simulations of turbulent flows

In this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3,700 are used to verify the accuracy and physical fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational Physic

Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an in-viscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space-and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations

Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an in-viscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space-and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations

Large-Eddy Simulations of Flow and Heat Transfer in Complex Three-Dimensional Multilouvered Fins

The paper describes the computational procedure and results from large-eddy simulations in a complex three-dimensional louver geometry. The three-dimensionality in the louver geometry occurs along the height of the fin, where the angled louver transitions to the flat landing and joins with the tube surface. The transition region is characterized by a swept leading edge and decreasing flow area between louvers. Preliminary results show a high energy compact vortex jet forming in this region. The jet forms in the vicinity of the louver junction with the flat landing and is drawn under the louver in the transition region. Its interaction with the surface of the louver produces vorticity of the opposite sign, which aids in augmenting heat transfer on the louver surface. The top surface of the louver in the transition region experiences large velocities in the vicinity of the surface and exhibits higher heat transfer coefficients than the bottom surface.Air Conditioning and Refrigeration Project 9