1Version, Date, POC Name

US Army Corpsof Engineers ®

Engineer Research and Development CenterUS Army Corpsof Engineers ®

Engineer Research and Development Center

Purpose: • To investigate multiscale flow discretizations

that •represent both the geometry and solution variable using variable-order polynomial and spline-based (NURBS) approximations•allow variable inter-element regularity

Product/Results:• Implement high-order polynomial and NURBS-

approximations in existing frameworks for Navier-Stokes (NS) and shallow water (SW) equations

• Initial adaptive strategies that exploit approximation order, mesh size, and regularity for NS and SW

• Application of adaptive strategies to challenging SW problems and initial free-surface isogeometric (NURBS) capability

Payoff:• High-order, accurate models for free surface

flows in complex geometries• New, efficient adaptive strategies for modeling

multiscale flows.

Schedule & Cost

Total $750K

MILESTONES FY10 FY11 FY12

Army 250 250 250 ($K)

• Implementation of High-Order FEMs

High-Order, multiscale flow simulation

• Adaptive, High-Order FEMs for NS and SW• Hybrid FEM strategies for SW and free-surface NS

21

Ending TRL/SRLs

Beginning TRL/SRLs

1

10

0

Variational multiscale simulation for 3-D

backward facing step

WP #

Status: New

2Version, Date, POC Name

US Army Corpsof Engineers ®

Engineer Research and Development CenterUS Army Corpsof Engineers ®

Engineer Research and Development Center

1. What is the problem? • It remains very difficult to represent many complex free-surface flows

accurately with existing low-order approximations given available computational resources.

• The objective of our research is to study multiscale flow discretizations that represent problem geometry and solution using variable-degree polynomial and spline-based (NURBS) approximations. Our approaches will also allow varying types and degrees of inter-element regularity.

2. What are the barriers to solving the problem? • The flow problems we are interested in are complex, turbulent free-

surface flows (hydrostatic or nonhydrostatic) in which capturing small scale variation is critical to overall accuracy.

• Unfortunately, gaining sufficient accuracy can be infeasible using standard low-order approximations.

• Higher order approximations can be more accurate, but traditional or naïve approaches have not been adequate for complex, engineering-scale problems.

3. How will you overcome these barriers?• Recent advancements have found effective ways to incorporate high-

order approximations into robust finite element frameworks for CFD.• We will explore two of these approaches: Isogeometric analysis and

discontinuous Galerkin approximations.• We will investigate high-order versions of each and investigate novel

hybrid combinations to test our hypothesis:•High-order approximations in the correct finite element framework will be much more efficient than existing low-order methods for many free-surface flows

• 4. What are the anticipated results and value of this research?• Isogeometric finite element approximations for laminar and turbulent channel

flows.• High-order, adaptive DG methods for shallow water flows.• Hybrid Isogeometric-DG strategies that exploit variable inter-element

regularity for improved efficiency.• 5. What is innovative about this work? • We will be exploring state-of-the-art computational methods for CFD that have

shown much promise, but have not been applied to free surface problems or real-world channel flows.

• We will be advancing methods that are very new and developing hybrid, adaptive approaches to make these techniques practical for engineering-scale problems.

• If we are successful, our approaches could revolutionize the way free-surface flows are modeled in the Corps and the community as a whole.

6. What is your publication plan? • Oct. 2010 - Hybrid isogeometric discontinuous Galerkin methods for open

channel flows. CMAME

• May. 2011 - Isogeometric analysis for microscale models of flow through permeable media. Physics of Fluids.

• Dec. 2011 - Mixed element hp refinement strategies for DG approximations of the shallow water equations. CMAME

• Oct. 2012 - Isogeometric level-set formulations for free-surface flows. JCP.

7. Transition plan:• We will be implementing and extending high-order isogeometric and DG

methods in our research codes. • A natural transition would be introduction of these techniquesinto production codes like ADH8. Collaboration across ERDC, commercial firms and/or academia:• CHL researchers will be collaborating academic researchers (Yuri Bazilevs at

UCSD)

High-Order, multiscale flow simulationWP #

Status: New

3Version, Date, POC Name

US Army Corpsof Engineers ®

Engineer Research and Development CenterUS Army Corpsof Engineers ®

Engineer Research and Development Center

High-Order, multiscale flow simulationWP #

Status: New

Funding ($K) FY10 FY11 FY12

Project 250 250 250

PI Co-PI Co-PI Dr. Matthew Farthing ERDC-CHL 601-634-2110 Matthew.W.Farthing@usace.army.mil

Dr. Chri s top h er Kees ERDC -CHL 601 -634 -3110 Christopher.E.Kees@usace.army.mil

Dr. Chri s top h er Massey ERDC -CHL 601 -634 -2406 Chris.Massey@usace..army.mil

Q1. What is the research problem? It remains very difficult to represent many complex free-surface flows accurately with existing low-order approximations given available computational resources.Q2. Describe the research objective. To advance classes of high-order accurate finite element approximations that have shown great promise for multiscale flow simulation.Q3. What is the toughest technical challenge in the work? High-order finite element approximations for nonlinear flow problems are complex. Isogeometric (NURBS-based) methods are in their infancy, and we are looking at developing strategies that are efficient for engineering problems.Q4. If successful, what will be the significance and impact of this research? Our approaches would add wholly new computational capabilities for hydrostatic and non-hydrostatic free surface flows. Q5. What future applications could result from this research? New software tools for flow modeling which can move directly from CAD geometries to analysisQ6. What other organizations are pursuing this research? These methods are actively being pursued in academiaQ7. What makes this research innovative, original and high risk? We will be exploring state-of-the-art computational methods for CFD that have shown much promise, but have not been applied to free surface problems or real-world channel flows. We will be advancing methods that are very new and developing hybrid, adaptive approaches to make these techniques practical for engineering-scale problems.Q8. How could this research develop future capabilities for ERDC? If we are successful, our approaches could revolutionize the way free-surface flows are modeled in the Corps and the community as a wholeQ9. Describe the research team and plan. The research team consists of PI’s from CHL and a leading expert in finite element method from academia. The research plan consists of three phases where begin by implementing methods for laminar flows then transition to adaptive techniques and turbulent problems.Q10. Is there adequate funding, equipment, and facilities to complete this research as planned? If funded at the expected level.