International Journal for Numerical Methods in Fluids

doi: 10.1002/fld.4864pmid: N/A

Liu, Xueliang; Wu, Haijun; Jiang, Weikang; Sun, Ruihua

doi: 10.1002/fld.4947pmid: N/A

A fast multipole boundary element method (FMBEM) in a subsonic uniform flow is presented. It is based on the boundary integral equation (BIE) in a subsonic uniform flow. The convected Green's function complicates its multipole expansion as well as the implementation of the computer code. Although the Lorentz transformation allows the Helmholtz equation in the uniform flow to be reduced to the standard Helmholtz equation, the deformation of the domain complicates the boundary conditions and may cause the elements' distortion. In this work, the analytical evaluations of singular integrals are achieved. Then a nonsingular BIE in a subsonic uniform flow is obtained and is incorporated in building FMBEM with the plane wave multipole expansion of Green's function directly. Details on the implementation of the algorithm are described. Numerical examples including a pulsating sphere radiation problem, a multibody scattering problem and an aircraft model are performed to validate the accuracy and efficiency of the proposed method. Results show that FMBEM solutions are in good agreement with analytical solutions. The difference between the analytical moments and numerical moments is also investigated carefully in the implementation of the fast multipole method. Dramatical improvements on solution efficiency are observed by comparing the developed algorithm with the CBEM.

Lochab, Ruchika; Kumar, Vivek

doi: 10.1002/fld.4948pmid: N/A

This article develops a new hybrid flux‐limited scheme for a numerical solution of the hyperbolic conservation laws by applying fuzzy logic‐based operator functions. The construction of the proposed flux‐limiter is explored using a fuzzy modifier function, having a suitable intensity. The purpose of this article is to present an efficient finite volume flux‐limited technique, derived from an entirely different subject of fuzzy mathematics, for tackling hyperbolic partial differential equations. Several standard test cases in one and two dimensions are solved numerically for demonstrating the robustness of the proposed new hybrid flux‐limited scheme.

Potghan, Nilesh; Jog, Chandrashekhar S.

doi: 10.1002/fld.4949pmid: N/A

In this work, we develop a numerical strategy for solving two‐phase immiscible incompressible fluid flows in a general arbitrary Lagrangian–Eulerian framework. As we use a conforming mesh moving with one of the fluids, there is no need to track or reconstruct the interface explicitly. A sharp interface, discontinuity in the fluid properties, and the jump in the pressure field are all accurately modeled using the dummy‐node technique. One of the challenges that this work addresses is to obtain a C0‐continuous approximation for the surface tension force term on the reference configuration, and to obtain its consistent linearization within the context of a Newton–Raphson strategy. It is shown by means of various numerical examples that the strategy is computationally efficient and robust, and circumvents the need for remeshing upto significantly large deformations.

Kikker, Anne; Kummer, Florian; Oberlack, Martin

doi: 10.1002/fld.4950pmid: N/A

A fully coupled high order discontinuous Galerkin (DG) solver for viscoelastic Oldroyd B fluid flow problems is presented. Contrary to known methods combining DG for the discretization of the convective terms of the material model with standard finite element methods (FEM) and using elastic viscous stress splitting (EVSS) and its derivatives, a local discontinuous Galerkin (LDG) formulation first described for hyperbolic convection‐diffusion problems is used. The overall scheme is described, including temporal and spatial discretization as well as solution strategies for the nonlinear system, based on incremental increase of the Weissenberg number. The solvers suitability is demonstrated for the two‐dimensional confined cylinder benchmark problem. The cylinder is immersed in a narrow channel with a blocking ratio of 1:2 and the drag force of is compared to results from the literature. Furthermore, steady and unsteady calculations give a brief insight into the characteristics of instabilities due to boundary layer phenomena caused by viscoelasticity arising in the narrowing between channel and cylinder.

Nawaz, Yasir; Arif, Muhammad Shoaib

doi: 10.1002/fld.4951pmid: N/A

A modification of Adams–Bashforth methods is given to construct time discretization schemes for partial differential equations. The second‐order modified method is shown to have a larger stability region than second‐order standard Adams–Bashforth for the two‐dimensional heat equation. Later the scheme is applied on considered flow problem in a square cavity. The flow problem is a modified mathematical model of the heat and mass transfer of mixed convection flow in a square cavity with effects of the inclined magnetic field and thermal radiations. In addition to this, another feature of the present contribution is to apply the coupling approach for employing a mixture of stable and unstable schemes. This coupling approach is based upon the difference quotient that has been used in the literature to construct flux limiters for reducing oscillations in the discontinuous solutions of hyperbolic conservation laws. Since proposed scheme produces oscillation in the beginning and then diverges for the chosen diffusion number that falls in the unstable region, so these oscillations, due to instability, is reduced by coupling it with the scheme that can produce the convergent solution. The convergence of the proposed scheme for the considered modified nondimensional mathematical model of mixed convection flow is also given. The improvement is shown in graphs when proposed second order in time scheme is compared with the standard second order in time Adams–Bashforth method. Also, the mixture of first‐order and unconditionally unstable Richardson's schemes is applied, and the solution is obtained, and some plots are provided.

Horníková, Hana; Vuik, Cornelis; Egermaier, Jiří

doi: 10.1002/fld.4952pmid: N/A

We deal with numerical solution of the incompressible Navier–Stokes equations discretized using the isogeometric analysis (IgA) approach. Similarly to finite elements, the discretization leads to sparse nonsymmetric saddle‐point linear systems. The IgA discretization basis has several specific properties different from standard FEM basis, most importantly a higher interelement continuity leading to denser matrices. We are interested in iterative solution of the resulting linear systems using a Krylov subspace method (GMRES) preconditioned with several state‐of‐the‐art block preconditioners. We compare the efficiency of the ideal versions of these preconditioners for three model problems (for both steady and unsteady flow in two and three dimensions) and investigate their properties with focus on the IgA specifics, that is, various degree and continuity of the discretization basis. Our experiments show that the block preconditioners can be successfully applied to the systems arising from high continuity IgA, moreover, that the high continuity can bring some benefits in this context. For example, some of the preconditioners, whose convergence is h‐dependent in the steady case, seem to be less sensitive to the mesh refinement for higher continuity discretizations. In the unsteady case, we generally get faster convergence for higher continuity than for C0 continuous discretizations of the same degree for most of the preconditioners.

Oyelakin, Ibukun S.; Adeyeye, Oluwaseun; Sibanda, Precious; Omar, Zurni

doi: 10.1002/fld.4953pmid: N/A

This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow and heat transfer characteristics between an actively controlled (AC) and a passively controlled (PC) nanoparticle concentration boundary is considered. The boundary value partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The system of ODEs is solved using a new block method without having to reduce the equivalent system to first‐order equations. The solutions are verified using the spectral local linearization method and further validation of the results is confirmed by comparing the current results, for some limiting cases, with those in existing literature. The solutions obtained using the block method are in good agreement with the solution obtained using the spectral local linearization method. The results are in good agreement with existing findings in previous studies. The solutions obtained using the AC and PC nanoparticle concentration boundary conditions are analyzed.

Zhang, Wanjia; Shih, Tom I‐P.

doi: 10.1002/fld.4954pmid: N/A

An adaptive method is developed to improve the accuracy of eddy‐viscosity Reynolds‐averaged‐Navier–Stokes (RANS) model in hybrid large‐eddy simulations (LES)‐RANS simulations by using available upstream LES results. The method first gets the tensorial eddy viscosity from the upstream LES solution at the LES‐RANS interface and then uses that information to improve the downstream RANS model by invoking the weak‐equilibrium assumption. The proposed method was evaluated via two test problems—flow in a channel and over a periodic hill. Results obtained show the proposed approach to increase the accuracy and stability of hybrid LES‐RANS simulations. Since the modification of the downstream RANS model is based on the tensorial eddy viscosity from the upstream LES solution, the method is adaptive to the problem being studied.

Klahn, Mathias; Madsen, Per A.; Fuhrman, David R.

doi: 10.1002/fld.4956pmid: N/A

This article presents a pseudospectral method for the simulation of nonlinear water waves described by potential flow theory in three spatial dimensions. The method utilizes an artificial boundary condition that limits the vertical extent of the fluid domain, and it is found that the reduction in domain size offered by the boundary condition enables the solution of the Laplace problem with roughly half the degrees of freedom compared to another spectral method in the literature for (wave number times water depth) kh≥2π. Moreover, it is found that the location of the artificial boundary condition can be chosen once and for all at the beginning of simulations such that the size of the fluid domain is reduced substantially, even when the lowest point of the free surface elevation varies significantly with time. The method is tested by simulating steady nonlinear wave trains, the development of crescent waves from a steady nonlinear wave train, a nonlinear focusing event, and a Gaussian hump which is initially at rest. It is shown that in all, but the most nonlinear cases, the method is capable of obtaining accurate results.