Spline-Characteristic Method for Simulation of Convective Turbulence

Malevsky, Andrei V.

doi:10.1006/jcph.1996.0037

Cited by 24 publications

(22 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Related methods which employ B-spline basis functions are due to Bermejo 9 and the spline±characteristic method for the simulation of thermal convection. 10 In the atmospheric sciences these numerical methods are known as semi-Lagrangian schemes. Staniforth and Co Ãte Â 11 present an overview of their use in atmospheric models.…”

Section: Introductionmentioning

confidence: 99%

Parallel algorithms for semi-lagrangian advection

Malevsky

Thomas

1997

Int. J. Numer. Meth. Fluids

View full text Add to dashboard Cite

Numerical time step limitations associated with the explicit treatment of advection‐dominated problems in computational fluid dynamics are often relaxed by employing Eulerian–Lagrangian methods. These are also known as semi‐Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at a Eulerian grid point. The value of the advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B‐splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high‐order ODE solver involving multiple interpolations of the velocity field. © 1997 John Wiley & Sons, Ltd.

show abstract

Section: Introductionmentioning

confidence: 99%

Parallel algorithms for semi-lagrangian advection

Malevsky

Thomas

1997

Int. J. Numer. Meth. Fluids

View full text Add to dashboard Cite

show abstract

“…The simplest semi-Lagrangian scheme with linear interpolation is equivalent to the classical first-order upwinding scheme [12], which is excessively dissipative (see [4] and [13]). A popular and effective choice for interpolation methods in previous works has been the cubic spline methods [14]; see also [15].…”

Section: Introductionmentioning

confidence: 99%

Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows

Xiu¹,

Sherwin

Dong³

et al. 2005

J Sci Comput

View full text Add to dashboard Cite

We present a review of the semi-Lagrangian method for advection-diffusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable.

show abstract

“…It has also been shown that the simplest semi-Lagrangian scheme with linear interpolation is equivalent to the classical first-order upwinding scheme [15], which is excessively dissipative (see [17] and [18]). A popular and effective choice for interpolation methods in previous works has been the cubic spline methods [10]; see also [2]. The idea of introducing high order characteristic methods has first been presented in [4] and it has been extended into the spectral frame in [9,7].…”

Section: Introductionmentioning

confidence: 99%

A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations

Xu¹,

Xiu²,

Karniadakis³

2001

View full text Add to dashboard Cite

We present a semi-Lagrangian method for integrating the three-dimensional incompressible NavierStokes equations. We develop stable schemes of second-order accuracy in time and spectral accuracy in space. Specifically, we employ a spectral element (Jacobi) expansion in one direction and Fourier collocation in the other two directions. We demonstrate exponential convergence for this method, and investigate the non-monotonic behavior of the temporal error for an exact three-dimensional solution. We also present direct numerical simulations of a turbulent channel-flow, and demonstrate the stability of this approach even for marginal resolution unlike its Eulerian counterpart. * Corresponding author, gk@cfm.brown.edu 1 Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

show abstract

Spline-Characteristic Method for Simulation of Convective Turbulence

Cited by 24 publications

References 17 publications

Parallel algorithms for semi-lagrangian advection

Parallel algorithms for semi-lagrangian advection

Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows

A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations

Contact Info

Product

Resources

About