Finite Volume Spatial Discretization Research Articles

Consistent hybrid finite volume/element formulations: model and complex viscoelastic flows

AbstractThe accuracy and consistency of a new cell‐vertex hybrid finite element/volume scheme are investigated for viscoelastic flows. Finite element (FE) discretization is employed for the momentum and continuity equation, with finite volume (FV) applied to the constitutive law for stress. Here, the interest is to explore the consequences of utilizing conventional cell‐vertex methodology for an Oldroyd‐B model and to demonstrate resulting drawbacks in the presence of complex source terms on structured and unstructured grids. Alternative strategies worthy of consideration are presented. It is demonstrated how high‐order accuracy may be achieved in steady state by respecting consistency in the formulation. Both FE and FV spatial discretizations are embedded in the scheme, with FV triangular sub‐cells referenced within parent triangular finite elements. Both model and complex flow problems are selected to quantify and assess accuracy, appealing to analysis and experimental validation. The test problem is that of steady sink flow, a pure extensional flow, which reflects some of the numerical difficulties involved in solving more generalized viscoelastic flows, where both source and flux terms may contribute equally to stress propagation. In addition, a complex transient filament‐stretching flow is chosen to compute the evolution of stress fields within liquid bridges. Shortcomings of the various stress upwinding schemes are discussed in this context, whilst dealing with such free‐surface type problems. Here, stress fluctuation distribution alone is advocated, and a Lax‐scheme is found to deliver accuracy and stability to the computational results, comparing well with the literature. Copyright © 2004 John Wiley & Sons, Ltd.

Development of unstructured dynamic grids for solving unsteady two-dimensional Euler equations

AbstractA method for the solution of the time dependent Euler equations on unstructured grids is presented for unsteady flows about oscillating aerofoils. The flow solver involves a finite volume spatial discretisation and a Runge-Kutta time-stepping scheme. A dynamic mesh algorithm is used for problems where the aerofoil moves and/or deforms. Steady and unsteady results are obtained for single and multi-element aerofoils.

Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aerodynamic analysis

An Euler solution algorithm is presented for unsteady aerodynamic analysis of complex-aircr aft configurations. The flow solver involves a multistage Runge-Kutta time-stepping scheme that uses a finite-volume spatial discretization on an unstructured grid made up of tetrahedra. A significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft. The mesh algorithm is a general procedure that can treat realistic motions and deformations of complex-aircraft configurations. Steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the Euler solver and dynamic mesh algorithm. The unsteady flow results were obtained for the aircraft oscillating harmonically in a complete-vehicle bending mode. Effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated. The paper presents descriptions of the Euler solver and dynamic mesh algorithm along with results that assess the capability.

Vortex-dominated conical-flow computations using unstructured adaptively-refined meshes

A conical Euler/Navier-Stokes algorithm is presented for the computation of vortex-dominated flows. The flow solver involves a multistage Runge-Kutta time stepping scheme which uses a finite-volume spatial discretization on an unstructured grid made up of triangles. The algorithm also employs an adaptive mesh refinement procedure which enriches the mesh locally to more accurately resolve the vortical flow features. Results are presented for several highly-swept delta wing and circular cone cases at high angles of attack and at supersonic freestream flow conditions. Accurate solutions were obtained more efficiently when adaptive mesh refinement was used in contrast with refining the grid globally. The paper presents descriptions of the conical Euler/Navier-Stokes flow solver and adaptive mesh refinement procedures along with results which demonstrate the capability.

Unsteady Euler airfoil solutions using unstructured dynamic meshes

Two algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis of oscillating airfoils. Both algorithms were developed for use on an unstructured grid made up of triangles. The first flow solver involves a Runge-Kutta time-stepping scheme with a finite-volume spatial discretization that reduces to central differencing on a rectangular mesh. The second flow solver involves a modified Euler time-integration scheme with an upwind-biased spatial discretization based on the flux-vector splitting of Van Leer. The paper presents descriptions of the Euler solvers and dynamic mesh algorithm along with results which assess the capability.

Solution of the Euler equations on unstructured grids for two-dimensional compressible flow

AbstractA method for the numerical solution of the two-dimensional Euler equations on unstructured grids has been developed. The cell-centred symmetric finite-volume spatial discretisation is applied in a general formulation that allows the use of arbitrary polygonal computational cells. The integration in time, to a steady-state solution, is performed using an explicit, multi-stage procedure, with standard convergence acceleration techniques such as local time stepping, enthalpy damping and implicit residual smoothing. Accuracy of solution, in terms of minimising spurious entropy production, is achieved through careful treatment of the artificial dissipative terms near boundaries. Standard test cases for both subcritical and supercritical flows, including single- and multi-element aerofoils have been used to validate the method.

Improvements to an Euler aerodynamic method for transonic flow analysis

Modifications to a three-dimensional Euler aerodynamic method (TEAM) and their effect on the accuracy of transonic flow simulations are described. TEAM'S solution algorithm is based on a finite-volume spatial discretization and multistage time-stepping algorithm to solve the Euler equations. Treatment of numerical dissipation and surface boundary condition are specifically addressed. The modified code includes the standard adaptive dissipation scheme using blended second and fourth differences and a flux-limited dissipation scheme. Improved treatment of the surface boundary condition minimizes spurious entropy production. TEAM computations are correlated with experimental data for two wings, ONERA M-6 and Wing C, and an arrow wing-body configuration. For Wing C, the TEAM predictions are also compared with those of the full-potential TWING code on identical grids.