Enthalpy Damping Research Articles

3D implicit mesh-less method for compressible flow calculations

An implicit mesh-less method is developed for calculation of compressible flows around three dimensional complex geometries. The algorithm is applied directly to the differential form of the governing equations using least-square formulation. A dual-time implicit time discretization scheme is developed, and the computational efficiency is enhanced by adopting accelerating techniques, such as local time stepping, residual smoothing and enthalpy damping. Two different artificial dissipation techniques are employed for stability preservation and it is shown that the scalar one is more efficient in terms of accuracy and computational time. The capabilities of the method are demonstrated by flow computations around different geometries under subsonic and transonic flow conditions. Results are presented which indicate good agreement with experimental and other reliable numerical data. The method is shown to reduce computational time by about 50% compared with the alternative explicit method.

An efficient implicit mesh‐less method for compressible flow calculations

AbstractA dual‐time implicit mesh‐less scheme is presented for calculation of compressible inviscid flow equations. The Taylor series least‐square method is used for approximation of spatial derivatives at each node which leads to a central difference discretization. Several convergence acceleration techniques such as local time stepping, enthalpy damping and residual smoothing are adopted in this approach. The capabilities of the method are demonstrated by flow computations around single and multi‐element airfoils at subsonic, transonic and supersonic flow conditions. Results are presented which indicate good agreements with other reliable finite‐volume results. The computational time is considerably reduced when using the proposed mesh‐less method compared with the explicit mesh‐less and finite‐volume schemes using the same point distributions. Copyright © 2010 John Wiley & Sons, Ltd.

Computation of three-dimensional transonic viscous flow using the JUMB03D code

A vertex based finite volume method for the solution of the three dimensional Reynolds averaged Navier-Stokes equations has been developed. The computations can be carried out blockwise after dividing the computational domain into smaller blocks to reduce the memory requirement for a single processor computer and also to facilitate parallel computing. A five stage Runge-Kutta scheme has been used to advance the solution in time. Enthalpy damping, implicit residual smoothing, local time stepping, and grid sequencing are used for convergence acceleration. In order to get smooth convergence for transonic, viscous flows, the artificial dissipation has been modified by using the time step for advective and diffusive equations. An algebraic turbulence model has been used to determine the turbulent eddy viscosity. The method has been used to compute transonic flow over a cropped delta wing and the ONERA M-6 wing, and subsonic flow over a launch vehicle configuration. The results obtained show good agreement with available experimental data.

Computation of three-dimensional transonic flow using a cell vertex finite volume method for the Euler equations

A cell vertex finite volume method for the solution of the three dimensional Euler equations has been developed. The computations can be carried out block-wise after dividing the computational domain into smaller blocks to reduce the memory requirement for a single processor computer and also to facilitate parallel computing. A five stage Runge-Kutta scheme has been used to advance the solution in time. Enthalpy damping, implicit residual smoothing, local time stepping, and grid sequencing are used for convergence acceleration. The solution procedure has been studied in detail by computing transonic flow over the ONERA M-6 wing, using both C-H and O-H type structured grids. The effects of changing the artificial viscosity parameters and the distance of the far field boundary are also investigated.

Enthalpy damping for high Mach number Euler solutions

An improvement on the enthalpy damping procedure currently in use in solving supersonic flow fields is described. A correction based on entropy values is shown to produce a very efficient scheme for simulation of high Mach number three-dimensional flows. Substantial improvements in convergence rates have been achieved by incorporating this enthalpy damping scheme in a finite-volume Runge-Kutta method for solving the Euler equations. Results obtained for blended wing-body geometries at very high Mach numbers are presented.

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.

A finite volume nodal point scheme for solving two dimensional Navier-Stokes equations

A finite volume nodal point spatial discretization scheme for the computation of viscous fluxes in two dimensional Navier-Stokes equations has been presented here. The present scheme gives second order accurate first derivatives and at least first order accurate second derivatives even for stretched and skewed grid. It takes almost the same numerical efforts to solve full Navier-Stokes equations as that for using thin layer approximation. The scheme has been implemented to solve laminar viscous flows past NACA0012 aerofoil. To advance the solution in time a five stage Runge-Kutta scheme has been used. To accelerate the rate of convergence to steady state, local time stepping, residual averaging and enthalpy damping have been employed. Only a fourth order artificial dissipation has been used here for global stability of the solution. A comparative study of the results obtained by the present scheme for full Navier-Stokes equations and for thin layer approximation have been made with other numerical methods developed earlier.

Efficient method for computing transonic and supersonic flows about aircraft

A numerical method for computing flow fields about fighter-type aircraft is described in this paper. The time-dependent Euler equations are discretized on a single-block mesh in finite volume form and integrated to steady state via a Runge-Kutta scheme with a local time step. Convergence is accelerated by employing enthalpy damping and residual smoothing in addition to a multigrid sequencing of the computational mesh. While specifically designed for application in the transonic regime, the method can be used efficiently even at supersonic and low-subsonic speeds. Very realistic fighter configurations can be handled as demonstrated by the examples presented.

Numerical solution of Navier-Stokes equations for two-dimensional viscous compressible flows

A nodal-point, finite-volume space discretization of viscous fluxes in compressible Navier-Stokes equations is presented. To advance the solution in time, an explicit five-stage Runge-Kutta scheme has been used. To accelerate the rate of convergence to steady state, local time stepping, residual averaging, and enthalpy damping have been employed. The scheme has been evaluated by solving laminar flow over a semi-infinite flat plate and an NACA 0012 air foil using thin-layer approximation. It has been observed here that fourth-order artificial dissipation is sufficient for numerical stability. The results have been compared with available theoretical and numerical solutions.

Solutions of the Euler equations for transonic and supersonic aircraft

A method for numerically computing steady incompressible flow fields about fighter-type aircraft at transonic and supersonic speeds is described. Discretization of the physical space around the aircraft is accomplished with a single-block H-O type mesh. The compressible Euler equations are discretized on this mesh using a fully conservative finite-volume method and are integrated to steady state via a five-stage Runge-Kutta scheme. The use of a maximum local time step, together with a residual smoothing technique and enthalpy damping, speeds up the solution process. Additional acceleration of convergence toward the steady state is provided by cycling the entire numerical scheme through coarser meshes in a multigrid sequence. The method is efficient and reliable. Examples of flow fields computed on a variety of aircraft at subsonic, transonic, and supersonic speeds are included.

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it has been proposed by Jameson, Schmidt, and Turkel to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed here, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which can move all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping can be effective in accelerating convergence to steady state.