Moab: Particle-Based Mesh-Free Code for Modeling Heat Transfer, Phase Transition, and Topological Changes in Liquids


Sandia National Laboratories (SNL)

Capability Expert

Lindsay Erickson, Karla Morris, Jeremy Templeton


Computational Tools and Modeling

Node Readiness Category

3: High-Temperature Electrolysis (HTE)
3: Low-Temperature Electrolysis (LTE)
3: Photoelectrochemical (PEC)
3: Solar Thermochemical (STCH)


Moab is a mesh-free physics code that uses the Reproducing Kernel Particle Method (RKPM – both point collocation and Gaussian quadrature approaches) to solve systems of equations. Moab calculates an error estimate and adjusts particle locations to minimize global solution error and utilizes a particle-level set method to describe and evolve interfacial dynamics. This package is built on top of Trilinos and uses Teuchos for memory management, Zoltan2 for parallel partitioning, as well as Tpetra and Belos for solving linear systems.

Capability Bounds‎

Because Moab utilizes Trilinos (Kokkos) it can be used on a variety of platforms from single processor, small machines to massively parallel computers, including advanced many-core and GPU architectures.

Unique Aspects‎

Moab does not require an underlying mesh; particles can adapt to the dynamics of a problem allowing for topological changes to be handled naturally. Moab targets multi-phase flow applications and can be extended to investigate hydrogen gas production from liquid water as well as modeling storage and safety scenarios (e.g. leaks). Moab solves thermal/mass transport at the continuum level and could capture the physics of hydrogen production and storage with the implementation of specific physics models to capture chemical and electrical reactions.


Moab is an LDRD research code under active development and has not yet been made publically available. Our objective is to make Moab available under an open source license, and this process can be expedited if necessary and would be accessible to consortium partners via GitHub. In its current form, Moab requires expert guidance for new users. Extensible canonical examples and tests are provided. Problem specification is created using text-based input files and geometries can be read in from Exodus or text format. Output is generated from Trilinos's Matrix Market Writer which can be read by SciPy and Matlab for visualization and post-processing.


Multi-scale modeling of reaction and transport phenomena in subcomponents and systems used for implementing water-splitting technologies will provide information useful for rational design of large scale hydrogen production plants.


Unlike most mesh-free methods, interior particles in Moab do not advect with the flow, which can lead to severe numerical errors. Rather, an error function is postulated and minimized, resulting in an ordered arrangement of particles for any configuration. Particles that define the interfaces move according to their physical (flow or phase transition) velocity to ensure the correct interface topology is captured.

Interior particles (circles) move according to an error minimization function in response to interfacial particles (x's) motion.

Using Moab to track a melting interface using a level set to solve the Stefan boundary value problem and RKPM equations to solve for the heat equation under shear flow conditions.

Particle level set method in Moab: Particles advect with a parabolic velocity profile and interfacial particles are randomly placed near the interface to increase accuracy.

Particle level set method for the rotating sphere test problem. Interface particles are placed inside (blue) and outside (red) the original interface and can be used to correct mass conservation errors due to level set advection.


NR Aluru. A point collocation method based on reproducing kernel approximations. International Journal for Numerical Methods in Engineering, 47(6):1083–1121, 2000.
D. Enright, R. Fedkiw, J. Ferziger and I. Mitchell. A hybrid particle level set method for improved interface capturing. J. Comp. Phys., vol. 193, pp. 83-127, 2002.
Wing Kam Liu, Sukky Jun, and Yi Fei Zhang. Reproducing kernel particle methods. International journal for numerical methods in fluids, 20(8-9):1081–1106, 1995.
M. Prakash, P Cleary, and J. Grandfield, Modelling of metal flow and oxidation during furnace emptying using smooth particle hydrodynamics. Journal of Material Processing Technology, vol 220, pp. 3396-3407, 2009.