Incompressible viscous fluid analysis around complex shapes using Isogeometric Analysis

This paper describes a computational model based on the dual reciprocity boundary element method (DRBEM) for the solution of two-dimensional incompressible viscous flow problems. The model is based on the Navier-Stokes equations in velocity-vorticity variables. The model includes the solution of vorticity transport equation for vorticity whose solenoidal vorticity components are obtained by solving Poisson equations involving the velocity and vorticity components. Both the Poisson equations and the vorticity transport equations are solved iteratively using DRBEM and combined to determine the velocity and vorticity vectors. In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Internal points are considered wherever solution is required. The model has been applied to simulate two-dimensional incompressible viscous flow problems with low Reynolds (Re) number in a typical square cavity. Results are obtained and compared with other models. The DRBEM model has been found to be reasonable and satisfactory.

Numerical investigations with eXtended isogeometric boundary element analysis (XIBEM) for direct and inverse Helmholtz acoustic problems

The present work is concerned with a study of numerical schemes for solving two-dimensional time-dependent incompressible free-surface fluid flow problems. The primitive variable flow equations are discretized by the finite difference method. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The diffusive terms are discretized by Implicit Backward and Crank- Nicolson schemes, and the non-linear advection terms are approximated by the high order upwind VONOS (Variable-Order Non-oscillatory Scheme) technique. In order to improved numerical stability of the schemes, the boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical schemes are then applied to the simulation of the Hagen-Poiseuille flow, and container filling problems. The results show that the semi-implicit techniques eliminate the stability restriction in the original explicit GENSMAC method.

Dynamic analysis of two-dimensional elasticity problems using the Isogeometric analysis method and its comparison with the finite element method is the subject of this research. For this purpose, formulation of the governing differential equation is obtained by using the B-spline basis functions. Some numerical examples employing consistent and lumped mass matrices are presented in order to compare the results of Isogeometric analysis and finite elements. The effect of increasing the number of control points and the degree of B-spline basis functions on the accuracy of the solution are also investigated. Furthermore, since the Newmark method is employed for transient dynamic analysis, the effects of parameters α and β on the solution accuracy are investigated. The obtained results demonstrate higher accuracy of the isogeometric analysis method in comparison with the FEM, despite employing fewer numbers of degrees of freedom and consequently reduction in the dimensions of system of equations and computational effort.

A number of special issues of this journal on computational fluid mechanics and fluid–structure interaction (FSI) were published in the past fiveyears. These special issues were very successful in terms of the kind of articles included and the attention those articles received following their publication. These research areas of computational mechanics, especially computational FSI, have seen major advances in method power and much expansion in computational challenges addressed. Advances in core computational technologies, including variational multiscale (VMS) methods, space–time (ST) techniques, and isogeometric analysis, and in special techniques targeting specific classes of problems, including biomechanics, parachute FSI, and wind-turbine modeling, played a key role in making that happen. All these motivated the dedication of one of the 25th anniversary special issues of the journal to computational fluid mechanics and FSI. The special issue includes papers focusing on different aspects of this class of problems, including method development, method analysis, meshing and remeshing, mesh refinement studies, computational efficiency, simulation-based analysis and design, verification and blending with experimental data, and industrial applications. The core and special methods presented include arbitrary Lagrangian–Eulerian (ALE) formulations, ST techniques,

This paper studies the nonlinear interactions between vortex-induced vibration of a spring-supported circular cylinder and the unsteady fluid flow in a narrow channel. The analytical model consists of two-dimensional incompressible viscous flow in a narrow channel at low Reynolds number, and the spring-supported cylinder that can move perpendicular to the wall of the channel. The marker-and-cell (MAC) method is used to calculate numerically the simultaneous equations governing the interaction between the motion of the cylinder and the unsteady fluid flow. Furthermore the numerical results are confirmed by experiments presented herein.

A numerical method is developed to solve the two-dimensional incompressible viscous flow with rotating boundaries of arbitrary shape using the boundary-fitted curvilinear coordinate transformation technique. The stream function-vorticity formulation is developed in which the requirement of the single-valuedness of the pressure is explicitly included to determine the boundary values of the stream function. The method is verified by the analysis of the flow between two long, eccentric cylinders. The method is also applied to the transient flow analysis in which the flow is driven by arbitrarily shaped rotating blades, and it is confirmed that the flow patterns can be successfully simulated using the proposed method even if the system has a moving boundary.

The process by which self-organization occurs for two-dimensional incompressible viscous flow in a friction-free box is investigated theoretically with the use of numerical simulations. It is shown by analytical and numerical eigenfunction spectrum analyses that two basic processes for the self-organization are the spectrum transfer by nonlinear couplings and the selective dissipation among the eigenmodes of the dissipative operator, and they yield spectrum accumulation at the lowest eigenmode. The third important process during nonlinear self-organization is an interchange between the dominant operators, which has hitherto been overlooked in conventional self-organization theories and which leads to a final self-similar coherent structure with the lowest eigenmode of the dissipative operator. \textcopyright{} 1996 The American Physical Society.

Head-based isogeometric analysis of transient flow in unsaturated soils

This study proposes a comprehensive optimization framework that integrates single- and multi-objective algorithms for solving complex problems in structural mechanics. A genetic algorithm (GA) and non-dominated sorting genetic algorithm II (NSGA-II) are developed and validated through multiple mechanical case studies, including truss structures, beam vibration and fluid-structure interactions. An isogeometric analysis (IGA) approach is incorporated to improve the accuracy of boundary representation. The numerical results demonstrate the robustness and precision of the proposed methods compared to existing literature, providing an efficient and reliable optimization strategy for practical engineering applications.

This research deals with the nonlinear interactions between unsteady fluid flow and vortex-induced vibration of a spring-supported circular cylinder in a narrow channel. The analytical model consists of two-dimensional incompressible viscous flow in a narrow channel at low Reynolds number, and the spring-supported cylinder that can move perpendicular to the wall of the channel. It is considered that synchronized measurement of unsteady fluid flow and motion of a body is very important when the nonlinear interaction between them is discussed.

A new space-time conservation element-solution element (CE/SE) scheme, which is based on the hexahedron mesh, is proposed by constructing a new structure of solution elements (SEs) and conservation elements (CEs) and extended to two-dimensional incompressible multiphase flows. This scheme is applied to several incompressible flow problems, such as lid-driven cavity flow, dam break flow, motions of falling droplets, flow instability and water-kerosene interaction. The numerical results and their comparison with lecture results and experimental data are presented. The comparisons demonstrate that the computational scheme developed currently is clear in physical concept, easy to be implemented and highly accurate and efficient for the above-mentioned problems. The highlight is that the pretreatment method is proposed, transforming the elliptic-parabolic equations to the hyperbolic equations, which can be directly simulated by the improved CE/SE scheme. Thus, the improved CE/SE scheme can be applied to incompressible multiphase flows widely.

A new numerical technique for two-dimensional incompressible flow problems combining the finite element method, which is best fitted to the flow analysis in an arbitrarily shaped flow geometry, and the finite difference method, which is advantageous in computing time and computer storage, is presented, aiming at realizing large-scale flow analysis inevitable for a detailed three-dimensional flow analysis and applying it to flow analysis around moving bodies. A modified ABMAC method is used as the basic algorithm, to which a sophisticated time integration scheme proposed by the present authors is applied. Numerical results including a moving boundary problem show good agreement with the experimental results.

In our previous research, the modified Galerkin method was proposed as one of the most efficient methods for the analyses of convection-diffusion problems and two-dimensional viscous fluid flow problems. In this modified Galerkin method, the inertia term is considered explicitly, so only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, we proposed a new finite element formulation for three-dimensional incompressible viscous fluid flow analysis. This formulation (‘MS’ algorithm and ‘MSR’ algorithm) is based on the modified Galerkin method coupled with the Semi-Implicit Method for Pressure-Linked Equations. The cubic cavity flow problems were investigated for the Reynolds number of 400, 1,000, 2,000 and 3,200 using non-uniform meshes. Finally, we confirmed the effectiveness of our proposed method through the comparison with other research works.

Stream function-vorticity driven cavity solution using p finite elements