Showing papers by "Eli Turkel published in 2006"
TL;DR: Finite difference schemes for the two-dimensional Helmholtz equation based on nine-point approximation have a sixth-order accurate local truncation order, compared with the standard five-point pointwise representation.
Abstract: We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncation order. The schemes are compared with the standard five-point pointwise representation, which has second-order accurate local truncation error and a nine-point fourth-order local truncation error scheme based on a Pade approximation. Numerical results are presented for a model problem.
76 citations
TL;DR: An unsteady Reynolds-averaged Navier-Stokes solver is applied for the simulation of a synthetic (zero net mass flow) jet created by a single diaphragm piezoelectric actuator in quiescent air.
Abstract: An unsteady Reynolds-averaged Navier-Stokes solver is applied for the simulation of a synthetic (zero net mass flow) jet created by a single diaphragm piezoelectric actuator in quiescent air. This configuration was designated as case 1 for the Computational Fluid Dynamics Validation 2004 (CFDVAL2004) workshop held at Williamsburg, Virginia, in March 2004. Time-averaged and instantaneous (phase-averaged) data for this case were obtained at NASA Langley Research Center, using multiple measurement techniques. Computational results from two-dimensional simulations with one-equation Spalart-Allmaras and two-equation Menter's turbulence models are presented along with the experimental data. The effect of grid refinement, preconditioning, and time-step variation are also examined.
32 citations
TL;DR: In this article, a multiple crack weight (MCW) method was proposed for the accurate and effective solution of strongly interacting cracks by meshless numerical methods, which constructs weight functions around cracks so that they simultaneously characterize all the cracks present in the single nodal domain of influence.
Abstract: SUMMARY 7 We devise a multiple crack weight (MCW) method for the accurate and effective solution of strongly interacting cracks by meshless numerical methods. The MCW method constructs weight functions 9 around cracks so that they simultaneously characterize all the cracks present in the single nodal domain of influence. This approach reduces the number of nodes necessary to achieve sufficient 11 accuracy and consequently it decreases the computational effort. Numerical examples demonstrate that the method allows an accurate solution of multiple cracks problems. Convergence of the method is 13 analysed and discussed. Copyright 2006 John Wiley & Sons, Ltd.
29 citations
TL;DR: This work reviews methods that instead use a continuous analysis and properties of the differential equation rather than the algebraic system, and presents the opposite case where the physical intuition can be used to develop improved algorithms.
Abstract: In many numerical procedures one wishes to improve the basic approach either to improve efficiency or else to improve accuracy. Frequently this is based on an analysis of the properties of the discrete system being solved. Using a linear algebra approach one then improves the algorithm. We review methods that instead use a continuous analysis and properties of the differential equation rather than the algebraic system. We shall see that frequently one wishes to develop methods that destroy the physical significance of intermediate results. We present cases where this procedure works and others where it fails. Finally we present the opposite case where the physical intuition can be used to develop improved algorithms.
14 citations
TL;DR: This work solves the Maxwell equations, with an interface between two media, using a fourth-order accurate algorithm, and regularizes the discontinuous dielectric permittivity by a continuous function either locally, near the interface, or globally, in the entire domain.
12 citations
TL;DR: This work presents an analysis and implementation of a fourth order accurate algorithm for the solution of Maxwell equations with an interface between two media and so the dielectric coefficient is discontinuous.
Abstract: Maxwell equations contain a dielectric coefficient ? that describes the particular media. For homogeneous materials the dielectric coefficient is constant. There is a jump in this coefficient across the interface between differing media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We present an analysis and implementation of a fourth order accurate algorithm for the solution of Maxwell equations with an interface between two media and so the dielectric coefficient is discontinuous. We approximate the discontinuous function by a continuous one either locally or in the entire domain. We study the one-dimensional system in frequency space. We only consider schemes that can be implemented for multidimensional problems both in the frequency and time domains.
7 citations
01 Jan 2006
TL;DR: For both 2-D and 3-D problems, it is demonstrated that the computational time of a well-tuned standard RK scheme can be reduced at least a factor of four.
Abstract: The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.
4 citations
TL;DR: In this paper, a new technique, the spiral weight, is introduced to increase the accuracy of the meshless approximations without increasing the nodal density, which is done by an appropriate modification of the weight function near crack tips.
Abstract: In the last decade several different approaches have been developed to study arbitrary static and dynamic cracks. Among these methods meshless techniques play an important role. These methods provide an accurate solution of a wide range of fracture mechanics problems while traditional methods such as finite element and boundary element have limitations. We wish to increase the accuracy of the meshless approximations without increasing the nodal density. This is done by an appropriate modification of the weight function near crack tips. Earlier attempts still had limitations that result in a lack of accuracy, especially in the case when a linear basis is used. In this work a new technique, the spiral weight, is introduced that minimizes the drawbacks of existing methods. Numerical examples show that the spiral weight method is more efficient than existing methods, when using a linear basis, for the solution of crack problems.
4 citations
Journal Article•
TL;DR: In this article, the simulation of a single diaphragm piezoelectric actuator in quiescent air was performed using an unsteady Reynolds-averaged Navier-Stokes (URANS) solver.
Abstract: We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for the simulation of a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. This configuration was designated as Case 1 for the CFDVAL2004 workshop held at Williamsburg, Virginia, in March 2004. Time-averaged and instantaneous data for this case were obtained at NASA Langley Research Center, using multiple measurement techniques. Computational results for this case using one-equation Spalart-Allmaras and two-equation Menter's turbulence models are presented along with the experimental data. The effect of grid refinement, preconditioning and time-step variation are also examined in this paper.
2 citations
06 Sep 2006
TL;DR: This work considers a multistage algorithm to advance in pseudo-time to find a steady state solution for the compressible Navier-Stokes equations, using an implicit preconditioner to approximate the numerical scheme.
Abstract: We consider a multistage algorithm to advance in pseudo-time to find a steady state solution for the compressible Navier-Stokes equations. The rate of convergence to the steady state is improved by using an implicit preconditioner to approximate the numerical scheme. This properly addresses the stiffness in the discrete equations associated with highly stretched meshes. Hence, the implicit operator allows large time steps i.e. CFL numbers of the order of 1000. The proposed method is applied to three dimensional cases of viscous, turbulent flow around a wing, achieving dramatically improved convergence rates.
1 citations