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Quantitative Methods in Defense & National Security “Understanding the Implications of Decoupling the Full Fluid Structure Interaction When Modeling Blast Waves Interacting with Structure” May 26, 2010. Motivating Problem. Example of a Blast-Structure Calculation using CTH. Time=400 m sec. - PowerPoint PPT Presentation

Motivating Problem

Example of a Blast-Structure Calculation using CTHTopEulerian code CTH well suited for detonationBlast-structure interaction for this problem is 3D in its behaviorDisparate length scales require Adaptive Mesh Refinement (AMR)Detonation, mm scaleAir shock, mm scaleBoat, 8 ft wideWith half plane symmetry ~1000 cpu-hours

Calculating Damage in LS-DYNA with CTH InputCTH is an Eulerian code suited for shock physicsLS-Dyna is a Lagrangian code suited for structural responseTimescale for the explosive loading is small relative to the timescale for structural responsei.e. The boat hull does not deform during blast loadingThis allows a combined code approachCTH + LS-DynaUse boat test data for validation

Issues with ApproachSimulation is split up into 2 separate calculations which are run consecutivelyThis approach precludes mutual interaction (inaccurate)This is inefficient from a parallelization standpointRequires loading histories on a rigid plate which is an engineering approximationWhat if the geometry was much more complicated?Not applicable for events involving long time behavior of structure (seconds)E.g. Sympathetic Detonation due to Kinetic TraumaRequires stand-alone routines to be written for specific application to allow CTH outputs to be read as LS-DYNA inputs time-consumingSimulation couples with commercial FEA solverScalability is limited by cost since licenses must be purchased for each processorSource code is not available to allow for seamless coupling independent of specific application

Some Technical Background

The Finite Volume Method

An Aside: The Small Cell Problem

Approach

Our Approach (in the large)Couple freely-available, scalable solvers using finite volume for the fluid (gas) and finite element for the solid structure focusing on the ability to handle complex geometryWrite an interface that passes information between the two solvers as part of a single simulationUse embedded boundary techniques in conjunction with state-of-the-art numerical routines capable of dealing with the associated, so-called, small cell problem

ApproachWrite 1D code to solve Euler equations with an ideal gas lawModify 1D code to allow for small cells (irregular grid) Implement new theoretical algorithm to deal with the small cell problemVerify and validate standard code and newly enhanced code through suite of linear and nonlinear test problemsApply code to fully coupled 1D fluid-structure interaction problem

1D Code for Studying Complex GeometryWritten in C, ~1000 lines of codeCompatible with CLAWPACK 1D input decksAllows for variable small-cell capabilitySolves 1D inviscid Euler equations:

1D Code for Studying Complex GeometryFully second order accurate (space and time)MUSCL-Hancock

Use and in the Riemann solver

TVD-preserving Runge-Kutta scheme

1D Code for Studying Complex GeometrySlope reconstruction routine allows for irregular gridsFollows recent work of BergerUses least squares solution

Van Leer slope limiter is used on primitive variableswith

1D Code for Studying Complex GeometryHLLC Riemann Solver Work of Toro, Spruce, and SpearesModifies HLL (Harten, Lax, and Van Leer) scheme by restoring missing contact and shear wavesApproximation for the intercell numerical flux is obtained directly in this approachShown to be effective in use with 1D inviscid Euler equations, for exampleRoe Solver

(Post Processing) Cell MergingDeveloped cell merging technique that occurs after the Riemann solve but still is conservativeFormulated and developed in 1DTake a normal time stepAfter Riemann Solve, merge small cell with a non-ghost neighbor in a volume-weighted wayPerform irregular grid slope reconstruction on merged cellDetermine correct state values at centers of small cell and neighbor cell based on the new slope calculatedSuccessfully demonstrated when small cells are present

Verification of 1D CodeConstant input stays constant (regular and small cell)Linear input stays linear (small cell)

Verification of 1D CodeSinusoidal advection preserved (regular and small cell) 200 cells on [-,] Fixed dt=.0005; tfinal=0.5

Verification of 1D CodeFully 2nd order accurate (regular grid)

Verification of 1D CodeSod shock tube problem verified (regular grid)

3000 cells

Verification (Courant Friedrichs)

Piston ProblemSimplest fluid-structure interaction problem (1D)Subramaniam Paper (Intl J Impact Engineering, 2009)Blast wave interacting with an elastic structure is analyzed in 1D within ALE frameworkThe effect of considering 2-way coupling in FSI is compared to 1-way coupling FSIBuilds on work of Blom (Comp. Meth. Appl. Mech. Engr., 1998)Advocates monolithical FSI algorithm

Transient Dynamic Analysis of Elastic Structure Consider a plate 4.5m in length, 2.25m wide, and 2.5cm thick Assume fixed edges on the plate and pinned BCs Can find equivalent structural mass and stiffness of the fundamental mode of vibration per unit cross sectional area:

Equation integrated with Newmark-Beta

Piston ProblemStructural displacement predicted by ignoring FSI is larger than the corresponding displacement considering FSI. Pressure history is qualitatively different as well:

Example Piston Problem PlotsPressure (1-way)Pressure (2-way)

ConclusionsThrough an entirely different approach, have qualitatively verified the work of Subramaniam, et al., in 1D:Distinct differences in pressure and displacement histories when comparing coupled and decoupled approaches1D case clearly demonstrates that the decoupling approach may be ill-advised for this class of problems (thin-walled structures)

Questions?