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International Journal for Uncertainty Quantification

Publication de 6  numéros par an

ISSN Imprimer: 2152-5080

ISSN En ligne: 2152-5099

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AN ALGORITHM FOR FAST CALCULATION OF FLOW ENSEMBLES

Volume 4, Numéro 4, 2014, pp. 273-301
DOI: 10.1615/Int.J.UncertaintyQuantification.2014007691
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RÉSUMÉ

This report presents an algorithm for computing an ensemble of p solutions of the Navier-Stokes equations. The solutions are found, at each timestep, by solving a linear system with one shared coefficient matrix and p right hand sides, reducing both storage required and computational cost of the solution process. The price that must be paid is a timestep condition involving the timestep and the size of the fluctuations about the ensemble mean. Since the method is a one step method and the timestep condition involves only known quantities, it can be imposed to adapt the next timestep. The report gives a comprehensive stability analysis, an error estimate, and some first tests.

CITÉ PAR
  1. Jiang Nan, Layton William, Numerical analysis of two ensemble eddy viscosity numerical regularizations of fluid motion, Numerical Methods for Partial Differential Equations, 31, 3, 2015. Crossref

  2. Jiang Nan, A Higher Order Ensemble Simulation Algorithm for Fluid Flows, Journal of Scientific Computing, 64, 1, 2015. Crossref

  3. Takhirov Aziz, Neda Monika, Waters Jiajia, Time relaxation algorithm for flow ensembles, Numerical Methods for Partial Differential Equations, 32, 3, 2016. Crossref

  4. Jiang Nan, Layton William, Algorithms and models for turbulence not at statistical equilibrium, Computers & Mathematics with Applications, 71, 11, 2016. Crossref

  5. Jiang Nan, A second-order ensemble method based on a blended backward differentiation formula timestepping scheme for time-dependent Navier-Stokes equations, Numerical Methods for Partial Differential Equations, 33, 1, 2017. Crossref

  6. Gunzburger Max, Jiang Nan, Schneier Michael, An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier--Stokes Equations, SIAM Journal on Numerical Analysis, 55, 1, 2017. Crossref

  7. Luo Yan, Wang Zhu, An Ensemble Algorithm for Numerical Solutions to Deterministic and Random Parabolic PDEs, SIAM Journal on Numerical Analysis, 56, 2, 2018. Crossref

  8. Jiang Nan, Schneier Michael, An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number, Numerical Methods for Partial Differential Equations, 34, 6, 2018. Crossref

  9. Gunzburger Max, Jiang Nan, Wang Zhu, An efficient algorithm for simulating ensembles of parameterized flow problems, IMA Journal of Numerical Analysis, 39, 3, 2019. Crossref

  10. Jiang Nan, Qiu Changxin, An efficient ensemble algorithm for numerical approximation of stochastic Stokes–Darcy equations, Computer Methods in Applied Mechanics and Engineering, 343, 2019. Crossref

  11. Li Ning, Fiordilino Joseph, Feng Xinlong, Ensemble Time-Stepping Algorithm for the Convection-Diffusion Equation with Random Diffusivity, Journal of Scientific Computing, 79, 2, 2019. Crossref

  12. Fiordilino J. A., A Second Order Ensemble Timestepping Algorithm for Natural Convection, SIAM Journal on Numerical Analysis, 56, 2, 2018. Crossref

  13. Gunzburger Max, Iliescu Traian, Schneier Michael, A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows, IMA Journal of Numerical Analysis, 40, 2, 2020. Crossref

  14. Luo Yan, Wang Zhu, A Multilevel Monte Carlo Ensemble Scheme for Random Parabolic PDEs, SIAM Journal on Scientific Computing, 41, 1, 2019. Crossref

  15. Chen Gang, Pi Liangya, Xu Liwei, Zhang Yangwen, A Superconvergent Ensemble HDG Method for Parameterized Convection Diffusion Equations, SIAM Journal on Numerical Analysis, 57, 6, 2019. Crossref

  16. He Xiaoming, Jiang Nan, Qiu Changxin, An artificial compressibility ensemble algorithm for a stochastic Stokes‐Darcy model with random hydraulic conductivity and interface conditions, International Journal for Numerical Methods in Engineering, 121, 4, 2020. Crossref

  17. Jiang Nan, A Pressure-Correction Ensemble Scheme for Computing Evolutionary Boussinesq Equations, Journal of Scientific Computing, 80, 1, 2019. Crossref

  18. Demir Medine, Kaya Songül, An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows, Applied Numerical Mathematics, 156, 2020. Crossref

  19. DeCaria Victor, Iliescu Traian, Layton William, McLaughlin Michael, Schneier Michael, An Artificial Compression Reduced Order Model, SIAM Journal on Numerical Analysis, 58, 1, 2020. Crossref

  20. Mohebujjaman Muhammad, Rebholz Leo G., An Efficient Algorithm for Computation of MHD Flow Ensembles, Computational Methods in Applied Mathematics, 17, 1, 2017. Crossref

  21. Ou Na, Lin Guang, Jiang Lijian, A Low-Rank Approximated Multiscale Method for Pdes With Random Coefficients, Multiscale Modeling & Simulation, 18, 4, 2020. Crossref

  22. Li Xue, Schiavazzi Daniele E., An ensemble solver for segregated cardiovascular FSI, Computational Mechanics, 68, 6, 2021. Crossref

  23. Su Haiyan, Feng Xinlong, Zhao Jianping, Penalty decoupled iterative methods for the stationary natural convection equations with different Rayleigh numbers, Applied Numerical Mathematics, 163, 2021. Crossref

  24. Jiang Nan, Li Ying, Yang Huanhuan, An Artificial Compressibility Crank--Nicolson Leap-Frog Method for the Stokes--Darcy Model and Application in Ensemble Simulations, SIAM Journal on Numerical Analysis, 59, 1, 2021. Crossref

  25. Rizzi Francesco, Parish Eric J., Blonigan Patrick J., Tencer John, A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems, Computer Methods in Applied Mechanics and Engineering, 384, 2021. Crossref

  26. Jiang Nan, Yang Huanhuan, SAV decoupled ensemble algorithms for fast computation of Stokes–Darcy flow ensembles, Computer Methods in Applied Mechanics and Engineering, 387, 2021. Crossref

  27. Jiang Nan, Li Ying, Yang Huanhuan, A second order ensemble method with different subdomain time steps for simulating coupled surface‐groundwater flows, Numerical Methods for Partial Differential Equations, 2021. Crossref

  28. Jiang Nan, Yang Huanhuan, Stabilized Scalar Auxiliary Variable Ensemble Algorithms for Parameterized Flow Problems, SIAM Journal on Scientific Computing, 43, 4, 2021. Crossref

  29. Layton William, Pei Wenlong, Qin Yi, Trenchea Catalin, Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow, Numerical Methods for Partial Differential Equations, 2021. Crossref

  30. Jiang Nan, Takhirov Aziz, Waters Jiajia, Robust SAV-Ensemble algorithms for parametrized flow problems with energy stable open boundary conditions, Computer Methods in Applied Mechanics and Engineering, 392, 2022. Crossref

  31. Jiang Nan, Qiu Changxin, Numerical analysis of a second order ensemble algorithm for numerical approximation of stochastic Stokes–Darcy equations, Journal of Computational and Applied Mathematics, 406, 2022. Crossref

  32. Mohebujjaman Muhammad, Wang Hongwei, Rebholz Leo G., Al Mahbub Md. Abdullah, An efficient algorithm for parameterized magnetohydrodynamic flow ensembles simulation, Computers & Mathematics with Applications, 112, 2022. Crossref

  33. Feng Xiaobing, Luo Yan, Vo Liet, Wang Zhu, An Efficient Iterative Method for Solving Parameter-Dependent and Random Convection–Diffusion Problems, Journal of Scientific Computing, 90, 2, 2022. Crossref

  34. Li Meng, Luo Xianbing, An EMC-HDG scheme for the convection-diffusion equation with random diffusivity, Numerical Algorithms, 90, 4, 2022. Crossref

  35. Carter John, Jiang Nan, Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number, Numerical Methods for Partial Differential Equations, 38, 5, 2022. Crossref

  36. Jiang Nan, Yang Huanhuan, Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations, Numerical Algorithms, 2022. Crossref

  37. Tosi Riccardo, Núñez Marc, Pons-Prats Jordi, Principe Javier, Rossi Riccardo, On the use of ensemble averaging techniques to accelerate the Uncertainty Quantification of CFD predictions in wind engineering, Journal of Wind Engineering and Industrial Aerodynamics, 228, 2022. Crossref

  38. Li Meng, Luo Xianbing, An ensemble Monte Carlo HDG method for parabolic PDEs with random coefficients, International Journal of Computer Mathematics, 2022. Crossref

  39. Jiang Nan, Yang Huanhuan, Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations, Advances in Computational Mathematics, 48, 5, 2022. Crossref

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