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Jan Nordström - One of the best experts on this subject based on the ideXlab platform.
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Stable and Accurate Filtering Procedures
Journal of Scientific Computing, 2020Co-Authors: Tomas Lundquist, Jan NordströmAbstract:High frequency errors are always present in numerical simulations since no difference stencil is accurate in the vicinity of the $$\pi $$ π -mode. To remove the defective high wave number information from the solution, Artificial Dissipation operators or filter operators may be applied. Since stability is our main concern, we are interested in schemes on summation-by-parts (SBP) form with weak imposition of boundary conditions. Artificial Dissipation operators preserving the accuracy and energy stability of SBP schemes are available. However, for filtering procedures it was recently shown that stability problems may occur, even for originally energy stable (in the absence of filtering) SBP based schemes. More precisely, it was shown that even the sharpest possible energy bound becomes very weak as the number of filtrations grow. This suggest that successful filtering include a delicate balance between the need to remove high frequency oscillations (filter often) and the need to avoid possible growth (filter seldom). We will discuss this problem and propose a remedy.
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conservative finite difference formulations variable coefficients energy estimates and Artificial Dissipation
Journal of Scientific Computing, 2006Co-Authors: Jan NordströmAbstract:Artificial Dissipation terms for finite difference approximations of linear hyperbolic problems with variable coefficients are determined such that an energy estimate and strict stability is obtained. Both conservative and non-conservative approximations are considered. The Dissipation terms are computed such that there is no loss of accuracy
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Stable Artificial Dissipation operators for finite volume schemes on unstructured grids
Applied Numerical Mathematics, 2006Co-Authors: Magnus Svärd, Jing Gong, Jan NordströmAbstract:Our objective is to derive stable first-, second- and fourth-order Artificial Dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilised.A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the Artificial Dissipation. Both a homogeneous Dissipation acting in all directions with equal strength and a modification that allows different amount of Dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.
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Stable and Accurate Artificial Dissipation
Journal of Scientific Computing, 2004Co-Authors: Ken Mattsson, Magnus Svärd, Jan NordströmAbstract:Stability for nonlinear convection problems using centered difference schemes require the addition of Artificial Dissipation. In this paper we present Dissipation operators that preserve both stability and accuracy for high order finite difference approximations of initial boundary value problems.
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Artificial Dissipation for Strictly Stable Finite Volume Methods on Unstructured Meshes
Computational Mechanics, 2004Co-Authors: Jing Gong, Magnus Svärd, Jan NordströmAbstract:In this thesis, the numerical solution of time-dependent partial differential equations (PDE) is studied. In particular high-order finite difference methods on Summation-by-parts (SBP) form are analysed and applied to model problems as well as the PDEs governing aerodynamics. The SBP property together with an implementation of boundary conditions called SAT (Simultaneous Approximation Term), yields stability by energy estimates. The first derivative SBP operators were originally derived for Cartesian grids. Since aerodynamic computations are the ultimate goal, the scheme must also be stable on curvilinear grids. We prove that stability on curvilinear grids is only achieved for a subclass of the SBP operators. Furthermore, aerodynamics often requires addition of Artificial Dissipation and we derive an SBP version. With the SBP-SAT technique it is possible to split the computational domain into a multi-block structure which simplifies grid generation and more complex geometries can be resolved. To resolve extremely complex geometries an unstructured discretisation method must be used. Hence, we have studied a finite volume approximation of the Laplacian. It can be shown to be on SBP form and a new boundary treatment is derived. Based on the Laplacian scheme, we also derive an SBP Artificial Dissipation for finite volume schemes. We derive a new set of boundary conditions that leads to an energy estimate for the linearised three-dimensional Navier-Stokes equations. The new boundary conditions will be used to construct a stable SBP-SAT discretisation. To obtain an energy estimate for the discrete equation, it is necessary to discretise all the second derivatives by using the first derivative approximation twice. According to previous theory that would imply a degradation of formal accuracy but we present a proof that this is not the case.
B. Lakshminarayana - One of the best experts on this subject based on the ideXlab platform.
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Numerical Simulation of Tip Clearance Effects in Turbomachinery
Journal of Turbomachinery, 1995Co-Authors: Anton Basson, B. LakshminarayanaAbstract:The numerical formulation developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes Artificial Dissipation, and is applicable to both viscous and inviscid flows. The value of this Artificial Dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure oftip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities as leakage mass flow, vortex strength, losses, dominant leakage flow regions, and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and Artificial Dissipation, that the tip clearance flow field can be captured accurately.
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An Artificial Dissipation Formulation for a Semi-Implicit Pressure Based Solution Scheme for Viscous and Inviscid Flows
International Journal of Computational Fluid Dynamics, 1994Co-Authors: Anton Basson, B. LakshminarayanaAbstract:SUMMARY The formulation of Artificial Dissipation terms for a semi-implicit, pressure based flow solver, similar to SIMPLE type formulations, is presented and is applied to both the Euler and the Navier-Stokes equations. The formulation uses generalized coordinates and a non-staggered grid. This formulation is compared to some SIMPLE and time marching formulations. The relationship between SIMPLE and time marching formulations is discussed briefly. The Artificial Dissipation inherent in some commonly used semi-implicit formulations, e.g. upwind differencing, powerlaw, QUICK and pressure weighting, is investigated. The scheme used here includes these Dissipation terms directly, but retains the ability to mimic previous schemes. The potential for errors introduced by the simultaneous use of Artificial Dissipation in the continuity equation and central differencing of convective terms, is revealed. The effect of the amount of Dissipation on the accuracy of the solution and the convergence rate is quantitativ...
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Numerical simulation of steady and unsteady viscous flow in turbomachinery using pressure based algorithm
1993Co-Authors: B. Lakshminarayana, A. BassonAbstract:The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes Artificial Dissipation, and is applicable to both viscous and inviscid flows. The values of these Artificial Dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and Artificial Dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of Artificial Dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake. The predicted unsteady wake profiles are compared with the available experimental data and the agreement is good. The numerical results are interpreted to draw conclusions on the unsteady wake transport mechanism in the blade passage.
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Numerical Simulation of Tip Clearance Effects in Turbomachinery
Volume 3B: General, 1993Co-Authors: Anton Basson, B. LakshminarayanaAbstract:The numerical formulation developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes Artificial Dissipation, and is applicable to both viscous and inviscid flows. The values of these Artificial Dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and Artificial Dissipation, that the tip clearance flow field can be captured accurately.Copyright © 1993 by ASME
Erik Burman - One of the best experts on this subject based on the ideXlab platform.
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Interior penalty variational multiscale method for the incompressible Navier-Stokes equation: Monitoring Artificial Dissipation
Computer Methods in Applied Mechanics and Engineering, 2007Co-Authors: Erik BurmanAbstract:In this paper, we apply the interior penalty method analyzed in [E. Burman and M.--A. Fernndez, Numer. Math. 107 (2007), no. 1, 39--77; MR2317827 (2008c:65317)] to flows at high Reynolds number. As a possible measure of solution quality we propose to monitor the ratio between the Artificial Dissipation induced by the numerical method and the computed physical Dissipation. For smooth flows we prove that for our method the Artificial Dissipation serves as an a posteriori error estimator and also that it vanishes at an optimal rate. In the case of flows with multiscale features, we discuss a heuristic approach relating the decay of the Artificial Dissipation to the decay rate of the power spectrum. Some numerical results in two space dimensions are presented examining the relation between the numerical Dissipation and solution quality.
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Interior penalty variational multiscale method for the incompressible Navier–Stokes equation: Monitoring Artificial Dissipation
Computer Methods in Applied Mechanics and Engineering, 2007Co-Authors: Erik BurmanAbstract:In this paper, we apply the interior penalty method analyzed in [E. Burman and M.--A. Fernndez, Numer. Math. 107 (2007), no. 1, 39--77; MR2317827 (2008c:65317)] to flows at high Reynolds number. As a possible measure of solution quality we propose to monitor the ratio between the Artificial Dissipation induced by the numerical method and the computed physical Dissipation. For smooth flows we prove that for our method the Artificial Dissipation serves as an a posteriori error estimator and also that it vanishes at an optimal rate. In the case of flows with multiscale features, we discuss a heuristic approach relating the decay of the Artificial Dissipation to the decay rate of the power spectrum. Some numerical results in two space dimensions are presented examining the relation between the numerical Dissipation and solution quality
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An Interior Penalty Variational Multiscale Method for High Reynolds Number Flows
Numerical Mathematics and Advanced Applications, 1Co-Authors: Erik BurmanAbstract:In this paper we present a framework using C° interior penalty methods for computations of the Navier-Stokes equations at high Reynolds number. The method is motivated by a formal scale separation argument and then justified by a priori error estimates. As a possible measure of solution quality we propose to monitor the ratio between the Artificial Dissipation induced by the numerical method and the computed physical Dissipation. We prove that for our method the Artificial Dissipation serves as an a posteriori error estimator.
Ayaboe Edoh - One of the best experts on this subject based on the ideXlab platform.
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Comparison of Artificial-Dissipation and solution-filtering stabilization schemes for time-accurate simulations
Journal of Computational Physics, 2018Co-Authors: Ayaboe Edoh, Nathan L. Mundis, Charles Merkle, Ann Karagozian, Venkateswaran SankaranAbstract:Abstract The current study investigates the use of solution filtering and Artificial Dissipation as stabilization methods for time-accurate computations, notably focusing on how the decoupling of Dissipation from integration impacts simulation error. Rewriting solution filtering in an effective Artificial-Dissipation form explicitly reveals the issue of temporal inconsistency, which is addressed by a proposed CFL re-scaling. In addition, expressing symmetric discrete filters as difference operators inspires the derivation of a “filter-based” Artificial-Dissipation formulation that provides the opportunity for direct spectral manipulation by utilizing known filter stencil specifications; this furthermore facilitates the creation of Pade-type Artificial Dissipation terms with spectrally tunable and scale-discriminant properties. Damping characteristics of the schemes are assessed through von Neumann analysis and are confirmed via simulations of the one-dimensional advection equation (wave-packet transport) as well as the three-dimensional compressible Navier–Stokes system (Taylor–Green vortex), where the impact of time step size on accuracy of the respective stabilization techniques is inspected.
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Highly-Accurate Filter-Based Artificial-Dissipation Schemes for Stiff Unsteady Fluid Systems
54th AIAA Aerospace Sciences Meeting, 2016Co-Authors: Nathan L. Mundis, Ayaboe Edoh, Venke SankaranAbstract:It is well known that the unmodified application of central difference schemes to the Euler equations produces numerically unstable results because such schemes do not naturally damp the high-frequency modes involved in odd-even decoupling. This shortcoming is usually overcome by adding Artificial-Dissipation terms, thereby producing stable schemes at the price of potential loss of solution accuracy. For unsteady fluid dynamics, solution filtering schemes have been proposed as a more accurate alternative to Artificial Dissipation especially when explicit physical-time integration is utilized. However, to solve computationally stiff problems efficiently, it is necessary to use a dual-time stepping approach, to which the application of solution filtering is not straightforward. Restricting the solution filtering only to the physical-time level does not guarantee numerical stability, as errors can accumulate in pseudo-time, causing divergence, while including it at the pseudo-time level introduces inconsistencies that lead to convergence problems. In the present work, Shapiroand Purser-type explicit solution filters are used to derive a new class of filter-equivalent Artificial-Dissipation operators that can be applied in pseudo time to produce stable, convergent, low-Dissipation solutions. These novel Artificial-Dissipation operators are shown to be indistinguishable from their corresponding filtering procedure for explicit, single-time schemes and are just as effective within a dual-time framework. In addition, the filter-based Artificial-Dissipation schemes are formulated for use with local preconditioning methods and applied to stiff problems such as low-Mach unsteady flows.
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Comparison of Artificial Dissipation and Filtering Schemes for Time-Accurate Simulations
53rd AIAA Aerospace Sciences Meeting, 2015Co-Authors: Ayaboe Edoh, Ann Karagozian, Charles MerkleAbstract:This study makes a comparison between Artificial Dissipation and filtering schemes as stabilization techniques for time-accurate fluid dynamics simulations. Specifically, we use von Neumann stability analysis to assess these alternatives in terms of their concurrent ability to maintain solution quality through proper preservation of low frequency content, while selectively damping high frequency errors. Our studies reveal the limitations of traditional Artificial Dissipation schemes as well as of explicit filtering procedures, while also providing a common framework to understand the relationship between these approaches. Importantly, we develop appropriate definitions of Pade-type (implicit) filtering procedures that have favorable properties for time-accurate computations over a wide range of time scales and Mach numbers.
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Optimal Numerical Schemes for Time Accurate Compressible Large Eddy Simulations: Comparison of Artificial Dissipation and Filtering Schemes
2014Co-Authors: Ayaboe Edoh, Charles Merkle, Ann Karagozian, Venke SankaranAbstract:Abstract : Objectives: Goal: Damp high frequency errors while preserving low wave content (i.e. low-pass response). (1) Compare damping character of Artificial Dissipation and Filtering. (2) formulate filter as an equivalent Artificial Dissipation scheme-- consequence of filter damping for stiff problems. (3) insight on achieving ideal low-pass response for general problems.
Anton Basson - One of the best experts on this subject based on the ideXlab platform.
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Numerical Simulation of Tip Clearance Effects in Turbomachinery
Journal of Turbomachinery, 1995Co-Authors: Anton Basson, B. LakshminarayanaAbstract:The numerical formulation developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes Artificial Dissipation, and is applicable to both viscous and inviscid flows. The value of this Artificial Dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure oftip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities as leakage mass flow, vortex strength, losses, dominant leakage flow regions, and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and Artificial Dissipation, that the tip clearance flow field can be captured accurately.
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An Artificial Dissipation Formulation for a Semi-Implicit Pressure Based Solution Scheme for Viscous and Inviscid Flows
International Journal of Computational Fluid Dynamics, 1994Co-Authors: Anton Basson, B. LakshminarayanaAbstract:SUMMARY The formulation of Artificial Dissipation terms for a semi-implicit, pressure based flow solver, similar to SIMPLE type formulations, is presented and is applied to both the Euler and the Navier-Stokes equations. The formulation uses generalized coordinates and a non-staggered grid. This formulation is compared to some SIMPLE and time marching formulations. The relationship between SIMPLE and time marching formulations is discussed briefly. The Artificial Dissipation inherent in some commonly used semi-implicit formulations, e.g. upwind differencing, powerlaw, QUICK and pressure weighting, is investigated. The scheme used here includes these Dissipation terms directly, but retains the ability to mimic previous schemes. The potential for errors introduced by the simultaneous use of Artificial Dissipation in the continuity equation and central differencing of convective terms, is revealed. The effect of the amount of Dissipation on the accuracy of the solution and the convergence rate is quantitativ...
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Numerical Simulation of Tip Clearance Effects in Turbomachinery
Volume 3B: General, 1993Co-Authors: Anton Basson, B. LakshminarayanaAbstract:The numerical formulation developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes Artificial Dissipation, and is applicable to both viscous and inviscid flows. The values of these Artificial Dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and Artificial Dissipation, that the tip clearance flow field can be captured accurately.Copyright © 1993 by ASME
