This page provides brief descriptions of specific simulation codes that are being used in development of a hybrid multiscale modeling system for subsurface simulations. These codes are defined on one of three generalized scales: Continuum, Pore and Sub-Pore. Currently we are focusing on the first two scales, but as the project proceeds we will expand to additional codes and scales.
Smoothed Particle Hydrodynamics (SPH)
SPH is a Lagrangian particle method for solving systems of partial differential equations. The Lagrangian particle nature of SPH allows physical and chemical effects to be incorporated into the modeling of flow processes with relatively little code-development effort. In addition, geometrically complex and/or dynamic boundaries and interfaces can be handled without undue difficulty. SPH was first introduced in the 1970s to simulate fluid dynamics in the context of astrophysical applications. Since its introduction, SPH has been successfully used to model a wide range of fluid flow processes and the behavior of solids subjected to large deformations.
Descriptions of the SPH method, extensions to the approach, code verification results, and application to pore-scale simulation of reactive transport (including precipitation/dissolution reactions) are given in several recent manuscripts published by project investigators:
- Tartakovsky, AM; Scheibe, TD; Meakin, P. 2009. Pore-scale model for reactive transport and biomass growth, JOURNAL OF POROUS MEDIA, 12(5): 417-434.
- Zhijie, X; Meakin, P: Tartakovsky, AM. 2009. Diffuse-interface model for smoothed particle hydrodynamics, PHYSICAL REVIEW E, 79, 036702.
- Tartakovsky, AM; Tartakovsky, DM; Scheibe, TD; Meakin, P. 2008. Hybrid simulations of reaction-diffusion systems in porous media, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 30(6):2799-2816.
- Tartakovsky, AM; Redden, G; Lichtner, PD; Scheibe, TD; Meakin, P. 2008. Mixing-induced precipitation: Experimental study and multi-scale numerical analysis, WATER RESOURCES RESEARCH, 44, W06S04.
- Tartakovsky AM; Meakin, P; Scheibe, TD; Eichler West, RM. 2007. Simulations of reactive transport and precipitation with smoothed particle hydrodynamics. JOURNAL OF COMPUTATIONAL PHYSICS 222(2):654-672.
- Tartakovsky, AM; Meakin, P. 2006. Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics. ADVANCES IN WATER RESOURCES 29 (10): 1464-1478.
- Tartakovsky, A; Meakin, P. 2005. Modeling of surface tension and contact angles with smoothed particle hydrodynamics. PHYSICAL REVIEW E 72(2).
- Tartakovsky, AM; Meakin, P. 2005. Simulation of unsaturated flow in complex fractures using smoothed particle hydrodynamics. VADOSE ZONE JOURNAL 4 (3): 848-855.
- Tartakovsky, AM; Meakin, P. 2005. A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh-Taylor instability. JOURNAL OF COMPUTATIONAL PHYSICS 207 (2): 610-624.
Results of a series of validation tests based on flow between two parallel plates are provided here.
Below is a visualization (created by Kwan-Liu Ma's Ultra-Scale Visualization group at UC Davis) of water particles in a 3D porous medium, calculated using PNNL's new parallel SPH code. In the visualization, fluid particles are colored by the local velocity magnitude, with red tones representing high velocity, and solid particles have been removed for visual clarity. This simulation used seven million computational particles and was run on the MPP2 supercomputer at PNNL's Environmental Molecular Sciences Laboratory using 500 processors.
Computational Fluid Dynamics (CFD)
Mesh-based (e.g., finite volume) numerical methods for simulating fluid flow in complex geometries have been applied to pore-scale flow simulation. We are using both commercially-available codes (e.g., StarCD) and our own in-house code (Tethys) to simulate these complex problems on parallel computing systems.
We have developed an animated visualization of computed flow in a wavy tube (analog for pore throats and pores in a porous medium). Right-click on the image below to download the movie to your local disk (WARNING: The animation file is large - over 90 Mbytes).
Below are some visualizations of streamlines (indicated by particle paths) and velocity distributions (colored plane) in simulated pore-scale flow systems.
Subsurface Transport Over Multiple Phases (STOMP)
STOMP is designed to be a general-purpose tool for simulating subsurface flow and transport. STOMP's target capabilities were guided by proposed or applied remediation activities at sites contaminated with volatile organic compounds and/or radioactive material. Developed with the support of the U.S. Department of Energy, Office of Environmental Restoration and Waste Management, the simulator's modeling capabilities address a variety of subsurface environments, including nonisothermal conditions, fractured media, multiple-phase systems, nonwetting fluid entrapment, soil freezing conditions, nonaqueous phase liquids, first-order chemical reactions, radioactive decay, solute transport, dense brines, nonequilibrium dissolution, and surfactant-enhanced dissolution and mobilization of organics.
The STOMP simulator solves the partial-differential equations that describe the conservation of mass or energy quantities by employing integrated-volume finite-difference discretization to the physical domain and backward Euler discretization to the time domain. The simulator has been written with a variable source code that allows the user to choose the solved governing equations (e.g., water mass, air mass, dissolved-oil mass, oil mass, salt mass, thermal energy). Depending on the chosen operational mode, the governing transport equations will be written over one to four phases (e.g., aqueous phase, gas phase, (nonaqueous phase liquid) NAPL phase, ice phase, solid phase). Solute transport, radioactive decay, and first-order chemical reactions are solved using a direct solution technique (e.g., Patankar's power-law formulation, (total variation diminishing) TVD scheme) following the solution of the coupled flow equations. Input is directed through semi-formatted text files and output is available through a variety of user-directed formats. The simulator recognizes a number of boundary condition types and allows their specification both internally and externally to the computational domain.