# Publications

This page collects peer-reviewed journal papers related to the algorithms implemented in Quinoa. The papers are grouped by executables.

## Walker

- J.R. Ristorcelli, J. Bakosi,
**A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence**, Journal of Turbulence, vol. 20, issue 7, Pages 393-423, 2019.This paper develops a statistical moment closure for mixing of two fluids with very different densities in a flow that becomes turbulent starting from a quiescent state. Developed using the Monte Carlo solutions from walker::

Beta , and walker::MixMassFractionBeta . - J. Bakosi, J.R. Ristorcelli,
**Diffusion Processes Satisfying a Conservation Law Constraint**, International Journal of Stochastic Analysis, vol. 2014, Article ID 603692, 9 pages, 2014.This paper develops a set of constraints that enables the development of statistical representations of

*N*non-negative continuous fluctuating variables satisfying a conservation principle. A practical example is*N*material mass fractions (that must always sum to unity) in a turbulent multi-material flow. Example model equations that satisfy such constraints are implemented in walker::Beta , walker::Dirichlet , and walker::GeneralizedDirichlet . - J. Bakosi, J.R. Ristorcelli,
**A stochastic diffusion process for Lochner's generalized Dirichlet distribution**, Journal of Mathematical Physics,*54*(10), 2013.This paper develops a system of stochastic differential equations whose statistically stationary solution is the generalized Dirichlet distribution. The system is implemented in walker::

GeneralizedDirichlet . - J. Bakosi, J.R. Ristorcelli,
**A stochastic diffusion process for the Dirichlet distribution**, International Journal of Stochastic Analysis, 2013, Article ID 842981, 2013.This paper develops a system of stochastic differential equations whose statistically stationary solution is the Dirichlet distribution. The system is implemented in walker::

Dirichlet . - J. Bakosi, J.R. Ristorcelli,
**Exploring the beta distribution in variable-density turbulent mixing**, Journal of Turbulence,*11*(37) 2010.This paper explores the beta distribution as a potential statistical representation of the fluctuating fluid density in variable-density turbulence and sets the stage for developing a probability density function model that can be useful for simulations of turbulent flows in which exactly computing all relevant spatial and temporal scales is not computationally economical. Implementations of various versions of the stochastic differential equation whose invariant is beta can be found in walker::

Beta , walker::NumberFractionBeta , walker::MassFractionBeta , walker::MixNumberFractionBeta , and walker::MixMassFractionBeta .

## Inciter

- A. Pandare, J. Waltz, J. Bakosi,
**A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces**, International Journal for Numerical Methods in Fluids, 2020: 1–25.This paper describes a discontinuous Galerkin method for multi-material flows in 1D, whose 3D version is currently being implemented in Quinoa.

- J. Waltz, N.R. Morgan, T.R. Canfield, M.R.J. Charest, L.D. Risinger, J.G. Wohlbier,
**A three-dimensional finite element arbitrary Lagrangian–Eulerian method for shock hydrodynamics on unstructured grids**, Computers & Fluids, 92: 172-187, 2014.This paper describes the hydro scheme implemented in Inciter as

`ALECG`

. - J. Waltz,
**Parallel adaptive refinement for unsteady flow calculations on 3D unstructured grids**, International Journal for Numerical Methods in Fluids, 46: 37–57, 2004.This paper describes the adaptive mesh refinement algorithm implemented in Inciter.