International Journal for Numerical Methods in Fluids
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Evaluation of discontinuous Galerkin and spectral volume methods for scalar and system conservation laws on unstructured grids Abstract The discontinuous Galerkin (DG) and spectral volume (SV) methods are two recently developed high‐order methods for hyperbolic conservation laws capable of handling unstructured grids. In this paper, their overall performance in terms of efficiency, accuracy and memory requirement is evaluated using a 2D scalar conservation laws and the 2D Euler equations. To measure their accuracy, problems with analytical solutions are used. Both methods are also used to solve problems with strong discontinuities to test their ability in discontinuity capturing. Both the DG and SV methods are capable of achieving their formal order of accuracy while the DG method has a lower error magnitude and takes more memory. They are also similar in efficiency. The SV method appears to have a higher resolution for discontinuities because the data limiting can be done at the sub‐element level. Copyright © 2004 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids - Tập 45 Số 8 - Trang 819-838 - 2004
Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks Abstract A numerical method based on radial basis function networks (RBFNs) for solving steady incompressible viscous flow problems (including Boussinesq materials) is presented in this paper. The method uses a ‘universal approximator’ based on neural network methodology to represent the solutions. The method is easy to implement and does not require any kind of ‘finite element‐type’ discretization of the domain and its boundary. Instead, two sets of random points distributed throughout the domain and on the boundary are required. The first set defines the centres of the RBFNs and the second defines the collocation points. The two sets of points can be different; however, experience shows that if the two sets are the same better results are obtained. In this work the two sets are identical and hence commonly referred to as the set of centres. Planar Poiseuille, driven cavity and natural convection flows are simulated to verify the method. The numerical solutions obtained using only relatively low densities of centres are in good agreement with analytical and benchmark solutions available in the literature. With uniformly distributed centres, the method achieves Reynolds number Re = 100 000 for the Poiseuille flow (assuming that laminar flow can be maintained) using the density of $11\times 11$ , Re = 400 for the driven cavity flow with a density of $33\times 33$ and Rayleigh number Ra = 1 000 000 for the natural convection flow with a density of $27\times 27$ . Copyright © 2001 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids - Tập 37 Số 1 - Trang 65-86 - 2001
Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows SUMMARY This paper presents a local moving least square‐one‐dimensional integrated radial basis function networks method for solving incompressible viscous flow problems using stream function‐vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square and one‐dimensional integrated radial basis function networks techniques. The major advantages of the proposed method include the following: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker‐δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local radial basis function approximations. Several examples including two‐dimensional (2D) Poisson problems, lid‐driven cavity flow and flow past a circular cylinder are considered, and the present results are compared with the exact solutions and numerical results from other methods in the literature to demonstrate the attractiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids - Tập 70 Số 11 - Trang 1443-1474 - 2012
A high‐order alternating direction implicit method for the unsteady convection‐dominated diffusion problem SUMMARY A high‐order alternating direction implicit (ADI) method for solving the unsteady convection‐dominated diffusion equation is developed. The fourth‐order Padé scheme is used for the discretization of the convection terms, while the second‐order Padé scheme is used for the diffusion terms. The Crank–Nicolson scheme and ADI factorization are applied for time integration. After ADI factorization, the two‐dimensional problem becomes a sequence of one‐dimensional problems. The solution procedure consists of multiple use of a one‐dimensional tridiagonal matrix algorithm that produces a computationally cost‐effective solver. Von Neumann stability analysis is performed to show that the method is unconditionally stable. An unsteady two‐dimensional problem concerning convection‐dominated propagation of a Gaussian pulse is studied to test its numerical accuracy and compare it to other high‐order ADI methods. The results show that the overall numerical accuracy can reach third or fourth order for the convection‐dominated diffusion equation depending on the magnitude of diffusivity, while the computational cost is much lower than other high‐order numerical methods. Copyright © 2011 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids - Tập 70 Số 6 - Trang 703-712 - 2012
Finite difference methods for solving the two‐dimensional advection–diffusion equation Abstract Using weighted discretization with the modified equivalent partial differential equation approach, several accurate finite difference methods are developed to solve the two‐dimensional advection–diffusion equation following the success of its application to the one‐dimensional case. These new methods are compared with the conventional finite difference methods in terms of stability and accuracy. The new methods are more accurate and often more stable than the conventional schemes.
International Journal for Numerical Methods in Fluids - Tập 9 Số 1 - Trang 75-98 - 1989
Multiscale method based on coupled lattice‐Boltzmann and Langevin‐dynamics for direct simulation of nanoscale particle/polymer suspensions in complex flows Summary A hybrid computational method coupling the lattice‐Boltzmann (LB) method and a Langevin‐dynamics (LD) method is developed to simulate nanoscale particle and polymer (NPP) suspensions in the presence of both thermal fluctuation and long‐range many‐body hydrodynamic interactions (HIs). Brownian motion of the NPP is explicitly captured by a stochastic forcing term in the LD method. The LD method is two‐way coupled to the nonfluctuating LB fluid through a discrete LB forcing source distribution to capture the long‐range HI. To ensure intrinsically linear scalability with respect to the number of particles, a Eulerian‐host algorithm for short‐distance particle neighbor search and interaction is developed and embedded to LB‐LD framework. The validity and accuracy of the LB‐LD approach are demonstrated through several sample problems. The simulation results show good agreements with theory and experiment. The LB‐LD approach can be favorably incorporated into complex multiscale computational frameworks for efficiently simulating multiscale multicomponent particulate suspension systems such as complex blood suspensions.
International Journal for Numerical Methods in Fluids - Tập 91 Số 5 - Trang 228-246 - 2019
Application of generalized differential quadrature to solve two‐dimensional incompressible Navier‐Stokes equations Abstract A global method of generalized differential quadrature is applied to solve the two‐dimensional incompressible Navier‐Stokes equations in the vorticity‐stream‐function formulation. Numerical results for the flow past a circular cylinder were obtained using just a few grid points. A good agreement is found with the experimental data.
International Journal for Numerical Methods in Fluids - Tập 15 Số 7 - Trang 791-798 - 1992
A simple sliding‐mesh interface procedure and its application to the CFD simulation of a tidal‐stream turbine SUMMARY An effective way of using computational fluid dynamics (CFD) to simulate flow about a rotating device—for example, a wind or marine turbine—is to embed a rotating region of cells inside a larger, stationary domain, with a sliding interface between. This paper describes a simple but effective method for implementing this as an internal Dirichlet boundary condition, with interfacial values obtained by interpolation from halo nodes. The method is tested in two finite‐volume codes: one using block‐structured meshes and the other unstructured meshes. Validation is performed for flow around simple, isolated, rotating shapes (cylinder, sphere and cube), comparing, where possible, with experiment and the alternative CFD approach of fixed grid with moving walls. Flow variables are shown to vary smoothly across the sliding interface. Simulations of a tidal‐stream turbine, including both rotor and support, are then performed and compared with towing‐tank experiments. Comparison between CFD and experiment is made for thrust and power coefficients as a function of tip‐speed ratio (TSR) using Reynolds‐averaged Navier–Stokes turbulence models and large‐eddy simulation (LES). Performance of most models is good near the optimal TSR, but simulations underestimate mean thrust and power coefficients in off‐design conditions, with the standard k – ϵ turbulence model performing noticeably worse than shear stress transport k – ω and Reynolds‐stress‐transport closures. LES gave good predictions of mean load coefficients and vital information about wake structures but at substantial computational cost. Grid‐sensitivity studies suggest that Reynolds‐averaged Navier–Stokes models give acceptable predictions of mean power and thrust coefficients on a single device using a mesh of about 4 million cells. Copyright © 2013 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids - Tập 74 Số 4 - Trang 250-269 - 2014
A Chimera method for the incompressible Navier–Stokes equations SUMMARY The Chimera method was developed three decades ago as a meshing simplification tool. Different components are meshed independently and then glued together using a domain decomposition technique to couple the equations solved on each component. This coupling is achieved via transmission conditions (in the finite element context) or by imposing the continuity of fluxes (in the finite volume context). Historically, the method has then been used extensively to treat moving objects, as the independent meshes are free to move with respect to the others. At each time step, the main task consists in recomputing the interpolation of the transmission conditions or fluxes. This paper presents a Chimera method applied to the Navier–Stokes equations. After an introduction on the Chimera method, we describe in two different sections the two independent steps of the method: the hole cutting to create the interfaces of the subdomains and the coupling of the subdomains. Then, we present the Navier–Stokes solver considered in this work. Implementation aspects are then detailed in order to apply efficiently the method to this specific parallel Navier–Stokes solver. We conclude with some examples to demonstrate the reliability and application of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids - Tập 75 Số 3 - Trang 155-183 - 2014
Sliding mesh algorithm for CFD analysis of helicopter rotor–fuselage aerodynamics Abstract The study of rotor–fuselage interactional aerodynamics is central to the design and performance analysis of helicopters. However, regardless of its significance, rotor–fuselage aerodynamics has so far been addressed by very few authors. This is mainly due to the difficulties associated with both experimental and computational techniques when such complex configurations, rich in flow physics, are considered. In view of the above, the objective of this study is to develop computational tools suitable for rotor–fuselage engineering analysis based on computational fluid dynamics (CFD). To account for the relative motion between the fuselage and the rotor blades, the concept of sliding meshes is introduced. A sliding surface forms a boundary between a CFD mesh around the fuselage and a rotor‐fixed CFD mesh which rotates to account for the movement of the rotor. The sliding surface allows communication between meshes. Meshes adjacent to the sliding surface do not necessarily have matching nodes or even the same number of cell faces. This poses a problem of interpolation, which should not introduce numerical artefacts in the solution and should have minimal effects on the overall solution quality. As an additional objective, the employed sliding mesh algorithms should have small CPU overhead. The sliding mesh methods developed for this work are demonstrated for both simple and complex cases with emphasis placed on the presentation of the inner workings of the developed algorithms. Copyright © 2008 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids - Tập 58 Số 5 - Trang 527-549 - 2008
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