# Presentation: 532336

## The slides that follow were presented at the PSAAP Bidder's Meeting May 16-17, 2006 and represent the ASC Trilab authors and interests as presented in the associated White Paper for this subject area.

- Predictive Science Academic Alliance Program (PSAAP)

## Turbulent Mixing and Hydrodynamics in the ASC Predictive Science Academic Alliance Program 

**Presented to:**
**Predictive Science Academic Alliance Program (PSAAP)**
**Bidders’ Meeting**
**Dallas/Fort Worth, TX**
**Oleg Schilling**
**Lawrence Livermore National Laboratory**
**16 May 2006**

## The ASC PSAAP is interested in research programs that broadly address compressible turbulent mixing and hydrodynamics relevant to the NNSA Laboratories

**We are interested in developing higher fidelity ****numerical simulation and predictive science-based multi-scale modeling**** capability for complex hydrodynamic flows**
**Primarily**** acceleration**** (Rayleigh-Taylor), ****shock**** (Richtmyer-Meshkov) and ****shear**** (Kelvin-Helmholtz) ****driven instabilities**
**Spatio-temporal ****evolution from**** (possibly unresolvable or poorly characterized) ****initial conditions, through linear and nonlinear phases, and finally to late-time turbulent phase**
**Multi-fluid**** ****hydrodynamics and mixing****: interpenetration, other multi-phase effects, and mixing/reaction at atomic scales**
**Flows are ****transitional**

**An overarching goal of these research efforts is to develop**
**and assess *****improved/more predictive models for instability***
***evolution, turbulent transport, mixing, and reactions***

## The design and interpretation of inertial confinement fusion (ICF) experiments requires a detailed understanding of compressible turbulent mixing

**Hydrodynamic instabilities exist at interfaces between**
**ablator shell**
**DT ice shell**
**cryogenic DT gas core**
**Instability growth and mixing**
**disrupt implosion symmetry**
**degrade fusion reaction**
**Mitigation of instabilities required to achieve ignition on NIF (National Ignition Facility)**

**Single-shell**
**ICF capsule**

## NIF capsule ignition designs minimize nonlinear,               and potentially, turbulent mixing of materials

**Cryogenic single-shell capsules designed to limit instabilities to weakly-nonlinear regime**
**Minimize mixing of burning fuel and cold pusher**
**Fabricating, transporting and fielding formidable**
**Double-shell capsules more easily manufactured**
**Outer shell efficiently absorbs x-rays, implodes    and collides with inner shell**
**Lower ignition temperatures**
**Requires smaller peak implosion speeds**
**Relaxed symmetry requirements**
**More susceptible to nonlinear instabilities and turbulent mixing**

**single-shell**

**double-shell**

## The complex hydrodynamic flows of interest are truly multi-scale, requiring tera/petascale (and beyond) computational resources

_**Multi-scale phenomena**_** of interest include**
**Growth and interaction of fluid structures**** from broadband, small-amplitude perturbations**
**Coupling between scales****, from the smallest to largest**
**Distribution of and interscale transfer of energy and scalar variance**
**Universal or flow-dependent scaling properties**
**These must be described using best possible numerical methods**
**Methods themselves should incorporate (or be consistent with) as many of these phenomena as possible**
**Or they should be augmented with predictive models for those phenomena not explicitly modeled by algorithms**
**Such numerical approaches include **_**direct numerical simulation**_** (DNS), **_**large-eddy simulation**_** (LES) and variants thereof, e.g., **_**MILES/ILES**_
**Models include ****instability growth****, ****subgrid-scale****, ****turbulent transport**** (RANS-type), ****probability/filtered density****, ****and related models**
***Other novel approaches***

***The need to model unresolved hydrodynamic and turbulent effects is a***
***manifestation of the closure problem of nonlinear statistical physics***

## Ensemble-averaging or explicit filtering of the nonlinear hydrodynamic equations lead to unclosed terms

**Closure problem for flows of interest is further complicated by**
**Presence of shocks and material discontinuities**
**Variable-density and compressibility effects**
**Highly nonequilibrium, inhomogeneous, anisotropic flow**
**Coexistence of multiple materials over wide range of thermodynamic and hydrodynamic conditions**
**Highly nonlinear terms (e.g., cross-sections, reaction terms)**
**Potentially unresolved initial conditions (e.g., ICF capsule shell perturbations)**
**Non-periodic boundaries and changing grid resolution, rendering explicit filtering problematic**
**Conventional gradient-diffusion *****N*****-equation (e.g., *****K*****-**********), higher-order closure (e.g., Reynolds stress) and subgrid-scale models have fundamental physical limitations**

***These difficulties push the limits on developing innovative models,***
***implementing them in complex codes on ASC computing platforms,***
***and quantitatively evaluating their predictions***

## Research on advanced hydrodynamic algorithm development is also required

**Complexity of flows of interest places stringent demands on underlying numerical methods**
**Adequate resolution of a very wide range of spatio-temporal scales (especially for scalars) requires accurate algorithms**
**Conditions typical of ICF applications demand robustness over a range of densities and other material properties**
**Complex geometry flows (e.g., in polyhedral hohlraums) necessitate unstructured, adaptive grids, and have complex boundary conditions**
**Shock propagation and interaction with material interfaces/mixing layers must be accurately captured**
**Hydrodynamics coupled to radiation transport and affected by material properties**
**Mixing and reactions occur on scales well below resolvable scales**

***The interaction/competition between the underlying hydrodynamics***
***and the processes modeled must also be considered***

## NNSA Laboratories primarily use adaptive mesh refinement (AMR) and arbitrary Lagrangian-Eulerian (ALE) methods to investigate hydrodynamics pertinent to modeling

**A full range of finite-difference, finite-volume, finite-element, particle and other methods (and hybrids thereof) is used**
**High-resolution (e.g., spectral/compact difference and non-oscillatory) methods also used to investigate specific turbulence issues**
**Dependence of quantities on numerical algorithm properties (e.g., order of flux reconstruction and resolution) being investigated**
***A priori***** and/or *****a posteriori***** model assessment against high fidelity DNS, other simulation data, and experiments is *****essential***
**Use of numerical analysis techniques to estimate errors etc.**
**Development of robust error estimation techniques can be useful**
**Development of infrastructure to **_**post-process**_** and **_**visualize**_** tera/petabyte-scale datasets also needed**

**Needed algorithm research includes:**
**determination of strengths, weaknesses and domains of applicability of methods; **
**evaluation of behavior of algorithms in complex codes, and;**
**development of new CFD algorithms to improve upon deficient algorithms**

## The development and assessment of transport and subgrid-scale models must be integrated with experimental data and verification/validation metrics

***These investigations push the limits on developing, executing and***
***diagnosing experiments relevant to model development, and***
***evaluating model implementations and accuracy of predictions***

**Rayleigh-Taylor turbulent transport and mixing is being investigated using DNS at LLNL**
**DNS models water channel experiment at Texas A&M**
**Uses parameterized initial conditions from experiment**
**Comparing DNS results to experimental measurements**
**Extracting quantities relating to RANS and second-order closure models from DNS**

**Late time**** DNS**** and ****experimental ****density variance spectrum**

**Time-evolution of anisotropy tensor components from DNS**

## High-resolution simulations provide data for transport, mixing and subgrid-scale model  assessment not currently available experimentally

**Richtmyer-Meshkov turbulent transport and mixing is also being investigated using MILES**
**9****th****-order WENO simulation models Mach 1.5 Vetter-Sturtevant experiment**
**Simulation uses a 2-mode initial perturbation with noise**
**Amplitude growth compared to experimental data and to reshock models**
**Extracting quantities relating to RANS and second-order closures**

***Before***** reshock**

***After***** reshock**

**Turbulent kinetic energy profile across layer**

**Pre- and post-reshock layer growth**

**Mass fraction isosurface from       513 ******** 257****2**** simulation**

**Also investigating effect of order**
**(5****th****-, 9****th****- and 11****th****-) on results**

## Collaboration among the Multidiscipline Simulation Centers (MSCs), Collaborating Research Activities (CRAs) and NNSA Laboratories is mutually beneficial

**Many synergistic collaborations with NNSA Laboratories are possible in the turbulent mixing and hydrodynamics disciplines**
**For example, it is useful to compare different approaches to**
**Hydrodynamics and simulating compressible turbulent mixing**
**Modeling unresolved turbulence, mixing and reactions**
**Work being done at NNSA Laboratories**
**Collaborators benefit by**
**Interactions with Laboratory experts**
**Multi-disciplinary training of students**
**Access to computing resources essential to these disciplines**
**Successful collaborations incorporate use of experimental data, coupled with appropriate validation/verification protocols**
**Refer to technical white paper**
**                    ****http://www.llnl.gov/asci/alliances/psaap/turb.pdf**
**   ****by Schilling (LLNL), Steinkamp (LANL) and Baer (SNL) for additional background**