High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes

Gawlik, Evan S.; Kabaria, Hardik; Lew, Adrian J.

doi:10.1002/nme.4891

Title: High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes

Abstract

Summary We propose a family of methods for simulating two‐dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle's boundary. The resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off‐the‐shelf time integrators. We demonstrate the approach by using Taylor‐Hood elements to approximate the fluid velocity and pressure. To integrate in time, we consider implicit Runge‐Kutta schemes as well as a fractional step scheme. We illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations. Copyright © 2015 John Wiley & Sons, Ltd.

Authors:

Gawlik, Evan S. ^[1]; Kabaria, Hardik ^[2]; Lew, Adrian J. ^[3]

Computational and Mathematical Engineering Stanford University CA USA
Mechanical Engineering Stanford University CA USA
Computational and Mathematical Engineering Stanford University CA USA, Mechanical Engineering Stanford University CA USA

Publication Date:: Thu Mar 26 00:00:00 EDT 2015

Sponsoring Org.:: USDOE

OSTI Identifier:: 1400702

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: International Journal for Numerical Methods in Engineering

Additional Journal Information:: Journal Name: International Journal for Numerical Methods in Engineering Journal Volume: 104 Journal Issue: 7; Journal ID: ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)

Country of Publication:: United Kingdom

Language:: English

Citation Formats


                    Gawlik, Evan S., Kabaria, Hardik, and Lew, Adrian J. High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes.  United Kingdom: N. p., 2015. 
Web.  doi:10.1002/nme.4891.

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                    Gawlik, Evan S., Kabaria, Hardik, & Lew, Adrian J. High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes.  United Kingdom.  https://doi.org/10.1002/nme.4891

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                    Gawlik, Evan S., Kabaria, Hardik, and Lew, Adrian J. Thu .  
"High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes".  United Kingdom.  https://doi.org/10.1002/nme.4891.

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@article{osti_1400702,

  title        = {High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes},

  author       = {Gawlik, Evan S. and Kabaria, Hardik and Lew, Adrian J.},

  abstractNote = {Summary We propose a family of methods for simulating two‐dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle's boundary. The resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off‐the‐shelf time integrators. We demonstrate the approach by using Taylor‐Hood elements to approximate the fluid velocity and pressure. To integrate in time, we consider implicit Runge‐Kutta schemes as well as a fractional step scheme. We illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations. Copyright © 2015 John Wiley & Sons, Ltd.},

  doi          = {10.1002/nme.4891},

  journal      = {International Journal for Numerical Methods in Engineering},

  number       = 7,

  volume       = 104,

  place        = {United Kingdom},

  year         = {Thu Mar 26 00:00:00 EDT 2015},

  month        = {Thu Mar 26 00:00:00 EDT 2015}

}

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Title: High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes

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Discontinuous Galerkin spectral element approximations on moving meshes journal, March 2011

Viscous flow with large free surface motion journal, August 1988

An unconditionally stable second-order accurate ALE-FEM scheme for two-dimensional convection-diffusion problems journal, September 2011

A Discontinuous Galerkin Method for the Navier-Stokes Equations on Deforming Domains using Unstructured Moving Space-Time Meshes conference, June 2013

The immersed boundary method journal, January 2002

Torsional springs for two-dimensional dynamic unstructured fluid meshes journal, September 1998

On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems journal, September 2005

A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries journal, November 2001

A high order Discontinuous Galerkin – Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes journal, August 2012

An immersed interface method for simulating the interaction of a fluid with moving boundaries journal, August 2006

High-order finite element methods for moving boundary problems with prescribed boundary evolution journal, August 2014

On the geometric conservation law for high-order discontinuous Galerkin discretizations on dynamically deforming meshes journal, May 2011

A Numerical Simulation of Vortex Shedding from an Oscillating Circular Cylinder journal, August 2002

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity journal, April 2009

The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction journal, July 2008

A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries journal, September 1997

Accurate Projection Methods for the Incompressible Navier–Stokes Equations journal, April 2001

Effects of Mesh Motion on the Stability and Convergence of ALE Based Formulations for Moving Boundary Flows journal, April 2006

Mesh deformation using the biharmonic operator journal, January 2003

An Adaptively Refined Cartesian Mesh Solver for the Euler Equations journal, January 1993

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations journal, November 2009

Improved ALE mesh velocities for moving bodies journal, October 1996

The Blob Projection Method for Immersed Boundary Problems journal, July 2000

An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges book, January 2005

An improved finite element space for discontinuous pressures journal, March 2010

A numerical solution of the Navier-Stokes equations using the finite element technique journal, January 1973

A cut-cell method for sharp moving boundaries in Cartesian grids journal, October 2013

A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations journal, August 2011

Mesh motion techniques for the ALE formulation in 3D large deformation problems journal, April 2004

Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces journal, November 1994

Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes: UNIVERSAL MESHES journal, March 2014

An efficient finite element method for embedded interface problems journal, April 2009

Robust and provably second-order explicit-explicit and implicit-explicit staggered time-integrators for highly non-linear compressible fluid-structure interaction problems journal, August 2010

Diffuse-Interface Methods in Fluid Mechanics journal, January 1998

Implicit Runge-Kutta Time Integrators for Fluid-Structure Interactions conference, June 2010

ALE formulation for fluid–structure interaction problems journal, November 2000

Immersed boundary method for flow around an arbitrarily moving body journal, March 2006

Flow structure from an oscillating cylinder Part 1. Mechanisms of phase shift and recovery in the near wake journal, June 1988

High-order temporal accuracy for 3D finite-element ALE flow simulations journal, September 2014

Une méthode d'approximation de la solution des équations de Navier-Stokes journal, January 1951

Stability and geometric conservation laws for ALE formulations journal, October 2004

Automatic monitoring of element shape quality in 2-D and 3-D computational mesh dynamics journal, May 2001

A conservative interface method for compressible flows journal, December 2006

A priori error estimates for the Arbitrary Lagrangian Eulerian formulation with finite elements
journal, January 2001

An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions
journal, September 1995

An accurate moving boundary formulation in cut-cell methods
journal, February 2013

Time-discrete higher order ALE formulations: a priori error analysis
journal, March 2013

High-Order Navier-Stokes Simulations Using a Sparse Line-Based Discontinuous Galerkin Method
conference, November 2012

Sharp interface Cartesian grid method I: An easily implemented technique for 3D moving boundary computations
journal, November 2005

Conservative interpolation between unstructured meshes via supermesh construction
journal, July 2009

Provably good mesh generation
journal, June 1994

A discontinuous-Galerkin-based immersed boundary method
journal, October 2008

A finite element method for the simulation of strong and weak discontinuities in solid mechanics
journal, August 2004

Stability analysis of second-order time accurate schemes for ALE–FEM
journal, October 2004

An implementation of singly-implicit Runge-Kutta methods
journal, September 1980

A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains
journal, March 2005

The Immersed Interface Method for the Navier–Stokes Equations with Singular Forces
journal, August 2001

High-Order LES Simulations using Implicit-Explicit Runge-Kutta Schemes
conference, June 2012

Sources of spurious force oscillations from an immersed boundary method for moving-body problems
journal, April 2011

A sliding mesh technique for the finite element simulation of fluid–solid interaction problems by using variable-node elements
journal, January 2014

High-order ALE schemes for incompressible capillary flows
journal, December 2014

Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity
journal, March 2006

Numerical solution of the Navier-Stokes equations
journal, January 1968

Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations
journal, October 2003

A Discontinuous Galerkin ALE Method for Compressible Viscous Flows in Moving Domains
journal, October 1999

An eXtended Finite Element Method/Lagrange multiplier based approach for fluid–structure interaction
journal, March 2008

Analysis of a Method to Parameterize Planar Curves Immersed In Triangulations
journal, January 2013

Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods
journal, February 2002

The fixed-mesh ALE approach applied to solid mechanics and fluid-structure interaction problems
journal, January 2009

Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations
journal, June 2000

Discontinuous Galerkin spectral element approximations on moving meshes
journal, March 2011

Viscous flow with large free surface motion
journal, August 1988

An unconditionally stable second-order accurate ALE-FEM scheme for two-dimensional convection-diffusion problems
journal, September 2011

A Discontinuous Galerkin Method for the Navier-Stokes Equations on Deforming Domains using Unstructured Moving Space-Time Meshes
conference, June 2013

The immersed boundary method
journal, January 2002

Torsional springs for two-dimensional dynamic unstructured fluid meshes
journal, September 1998

On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems
journal, September 2005

A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries
journal, November 2001

A high order Discontinuous Galerkin – Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes
journal, August 2012

An immersed interface method for simulating the interaction of a fluid with moving boundaries
journal, August 2006

High-order finite element methods for moving boundary problems with prescribed boundary evolution
journal, August 2014

On the geometric conservation law for high-order discontinuous Galerkin discretizations on dynamically deforming meshes
journal, May 2011

A Numerical Simulation of Vortex Shedding from an Oscillating Circular Cylinder
journal, August 2002

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity
journal, April 2009

The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction
journal, July 2008

A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
journal, September 1997

Accurate Projection Methods for the Incompressible Navier–Stokes Equations
journal, April 2001

Effects of Mesh Motion on the Stability and Convergence of ALE Based Formulations for Moving Boundary Flows
journal, April 2006

Mesh deformation using the biharmonic operator
journal, January 2003

An Adaptively Refined Cartesian Mesh Solver for the Euler Equations
journal, January 1993

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations
journal, November 2009

Improved ALE mesh velocities for moving bodies
journal, October 1996

The Blob Projection Method for Immersed Boundary Problems
journal, July 2000

An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges
book, January 2005

An improved finite element space for discontinuous pressures
journal, March 2010

A numerical solution of the Navier-Stokes equations using the finite element technique
journal, January 1973

A cut-cell method for sharp moving boundaries in Cartesian grids
journal, October 2013

A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations
journal, August 2011

Mesh motion techniques for the ALE formulation in 3D large deformation problems
journal, April 2004

Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces
journal, November 1994

Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes: UNIVERSAL MESHES
journal, March 2014

An efficient finite element method for embedded interface problems
journal, April 2009

Robust and provably second-order explicit-explicit and implicit-explicit staggered time-integrators for highly non-linear compressible fluid-structure interaction problems
journal, August 2010

Diffuse-Interface Methods in Fluid Mechanics
journal, January 1998

Implicit Runge-Kutta Time Integrators for Fluid-Structure Interactions
conference, June 2010

ALE formulation for fluid–structure interaction problems
journal, November 2000

Immersed boundary method for flow around an arbitrarily moving body
journal, March 2006

Flow structure from an oscillating cylinder Part 1. Mechanisms of phase shift and recovery in the near wake
journal, June 1988

High-order temporal accuracy for 3D finite-element ALE flow simulations
journal, September 2014

Une méthode d'approximation de la solution des équations de Navier-Stokes
journal, January 1951

Stability and geometric conservation laws for ALE formulations
journal, October 2004

Automatic monitoring of element shape quality in 2-D and 3-D computational mesh dynamics
journal, May 2001

A conservative interface method for compressible flows
journal, December 2006