High-Order Overset for Moving Grids · Flux points on arti cial boundary faces - Arti cial Boundary...

Introduction Overset Method Results

High-Order Overset for Moving Grids2017 Aero/Astro Industrial Affiliates Meeting

J. Crabill, A. Jameson

Aerospace Computing Laboratory, Stanford University

April 19, 2017

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 1/20

Introduction Overset Method Results

Outline

1 Introduction

2 Overset Method

3 Results

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 2/20

Introduction Overset Method Results

Outline

1 IntroductionMotivationWhy High-Order?(Direct) Flux Reconstruction Basics

2 Overset Method

3 Results

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 2/20

Introduction Overset Method Results

Background: Overset-Grid CFD

Problem: Complex geometries in relative motion

Solutions:

Constant re-meshingMesh DeformationOverset Grids: One grid per body of interest

Well-established approachSimplifies mesh generationNot conservative - Introduces error withinter-grid interpolation

[DARCorp]

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 3/20

Introduction Overset Method Results

Why Use High-Order?

Higher accuracy per DOF

Less dissipative: Better at preservingunsteady, vortex-dominated flows

Better suited for utilizing modernhardware

[NASA]

Previous work has shown high-order + overset retainshigh-order accuracy [1] [2]

Current work: Show high-order overset is accurate and efficient onmoving grids and complex geometries

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 4/20

Introduction Overset Method Results

Direct Flux Reconstruction (DFR) Basics

Similar in concept to many finite-element methods

Solution defined at multiple solution points inside each element

Solution point values used to construct element-wide polynomials

Conservation enforced at flux points with common flux functions(i.e. Riemann solvers)

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 5/20

Introduction Overset Method Results

Outline

1 Introduction

2 Overset MethodOverset Hole CuttingArtificial Boundary (AB) Method

3 Results

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Introduction Overset Method Results

Hole Blanking / Boundary Creation

Example CFD application: Flow around airfoil

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Introduction Overset Method Results

Hole Blanking / Boundary Creation

With overset method, only small grid local to airfoil required

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Introduction Overset Method Results

Hole Blanking / Boundary Creation

Remainder of domain filled in with background grid

(Typically a structured or pseudo-structured grid)

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Introduction Overset Method Results

Hole Blanking / Boundary Creation

Must remove elements from background grid where airfoil isAll nodes within solid boundary marked as hole nodes

Remaining overlapping points marked as fringe/receptor nodes

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Introduction Overset Method Results

Traditional Hole Cutting

Traditional finite-volume: interpolate to nodes (dual-cell centroids)

(Volume Interpolation)

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 10/20

Introduction Overset Method Results

High-Order Hole Cutting

High-Order Overset: No fringe/receptor nodes neededOnly require that grids have a continuous overlapping boundary

(Surface Interpolation)

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 11/20

Introduction Overset Method Results

Hole Blanking / Boundary Creation

Flux points on artificial boundary faces - Artificial Boundary FluxPoints - are only points requiring data interpolation

Less interpolation required than for volume approachNatural extension of discontinuous finite-element methods

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 12/20

Introduction Overset Method Results

Fringe Point Connectivity

Donor cells found using fast search algorithm (i.e., binary tree)

Iterative method used to find reference position

For moving grids, search + iteration required at every time step

Connectivity for all points done in parallel on accelerator

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 13/20

Introduction Overset Method Results

Artificial Boundary Method

Data interpolated to faces as external / “right” state

Interface flux / Riemann solver used as normal

Grids ”unaware” of any special computation occurring

Dubbed the Artificial Boundary approach [2]

1D Example

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Introduction Overset Method Results

Outline

1 Introduction

2 Overset Method

3 ResultsTaylor-Green VortexPerformance ComparisonConclusion and Future Work

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 14/20

Introduction Overset Method Results

Taylor-Green Vortex

High-Order Workshop “difficult”-level test case [3]

3 overset grid computations performed for comparison:

1 Inner grid static2 Inner grid translating in 3D figure-8 pattern3 Inner grid rotating around arbitrary axis

Elements added/removed from background grid as inner grid moves

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 15/20

Introduction Overset Method Results

Taylor-Green Vortex

Comparing to 5th-order reference solution generated by PyFR [4]

Excellent agreement even with continual blanking/unblanking

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 16/20

Introduction Overset Method Results

Performance Comparison

Overhead less than 2x over single, static grid

(P=4)

Run using the Taylor-Green test case

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 17/20

Introduction Overset Method Results

Summary

High-order overset code developed

High-order accuracy retained

Minimal overhead for complex, dynamic calculations

Future Work:

Develop high-order-specificconnectivity algorithms

Near-Term Case: Golf Ball

Reynold’s Number: 180,000Mach Number: .2Difficult Re to modelPlan to utilize overset to simulatespinning golf-ball trajectory

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Introduction Overset Method Results

Questions?

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Introduction Overset Method Results

References I

Crabill, J., Sitaraman, J., and Jameson, A., “A High-Order OversetMethod on Moving and Deforming Grids,” AIAA AviationConference, 2016.

Galbraith, M. C., A Discontinuous Galerkin Overset Solver , Ph.D.thesis, University of Cincinatti, 2013.

“2nd International Workshop on High-Order CFD Methods,” 2013.

Witherden, F. D., Farrington, A. M., and Vincent, P. E., “PyFR: AnOpen Source Framework for Solving Advection-Diffusion TypeProblems on Streaming Architectures using the Flux ReconstructionApproach,” Computer Physics Communications, Vol. 185, 2014,pp. 3028–3040.

J. Crabill, A. Jameson 2017 Aero/Astro Affiliates Meeting 20/20