Objective

Much of our current knowledge of the eruptive history and evolution of Earth's basaltic volcanoes, and of the thermal evolution and volcanic resurfacing rates for all of the terrestrial planets, is based on estimates of lava flow rates and rheologies from lava flow morphologies. However, the processes that interact to produce flow morphology are poorly understood. The problem is complex, and most modeling efforts can examine only small segments of it.

Essentially, the lava fluid and flow fields are strongly coupled through a complex rheology (flow behavior) that evolves through several regimes of temperature and shear-rate dependence. Analytic models and serial versions of the current fluid dynamics software are inadequate for tracking the resulting steep gradients in temperature and material properties through either space or time. Our understanding of the basic flow and cooling processes and their dependencies on cooling environment (submarine, subaerial, or Venusian or Martian), is thus severely limited.

This study addresses the problem with a realistic, temperature-dependent and shear-rate dependent flow rheology, 3-D flow geometry, and thermal boundary conditions to examine cooling and flow differences under different planetary thermal conditions.

Approach

This study builds from our serial processor results for isothermal lava flow simulations to more realistic temperature- and time-dependent simulations. It also tests the ability of the software and hardware to handle the complex material behaviors often encountered in Earth sciences applications. Our preliminary work has been with isothermal, 3-D lava flows with a shear-dependent rheology and has resulted in a general flow solution for the flow rate as a function of rheology parameters, flow shape, etc. (Sakimoto and Deane, in preparation). More realistic time and temperature-dependent simulations are considered here with fully temperature- and shear-dependent rheologies, with an expanded flow domain to track down-flow changes, and a solid flow base to track heat flow from the lava into the underlying terrain.

We use the Spectral Element Method (SEM) to obtain highly accurate solutions. The SEM considers hexahedral (brick) type elements with Nth order Gauss-Legendre interpolation polynomial representation in each of the three directions in each element. Several aspects of the intended problem push it out of the realm of serial processing. The expansion of the domain to track down flow changes, and the addition of time dependence and a solid base, require a moderate to large increase in computational requirements.

The largest computational requirement is in the resolution of the mesh. Since both field observations and lava rheology models predict large temperature changes and thus rheology changes (1 to 10 orders of magnitude) across a typical lava flow margin, the number of elements required for temperature-dependent models is substantially larger than that required for our previous isothermal simulations. However, the results will tell us much more about lava flow processes than our isothermal simulations, since it is these large gradients in temperature and rheology that drive most of the flow processes in real flows.

Accomplishments

This composite figure shows three runs illustrating the effect of cooling on non-isothermal channel flow simulation of surface lava flow. Flow is from left to right. Simulations were performed on the CRAY T3E, time-evolving to a steady state. The top figure shows an isometric view of the temperature contours in the right half of the lava channel. The lower set of figures illustrates the effect of increased surface cooling: The layer equilibrates at shorter distances from the inflow. The spectral element grid has 1,200 3-D elements each with a 7th order polynomial representation. Inflow conditions were imposed on the left where fluid at T=1413 K flows in. The top of the layer is maintained at T=673 K. The plane closest to the reader is a plane of symmetry, while the opposite plane is a wall maintained, as is the bottom, at T=1373 K. The slope of the layer is 3.5 degrees. From these calculations we are able to determine the time and distance from the inflow that is a function of the cooling.

Significance

These are the first 3-D simulations of cooling surface lava flows.

Status/Plans

The illustrated flow above shows a Newtonian flow. We are currently making the viscosity law non-Newtonian, and these results will be available shortly. We also plan to use our existing solutions for 3-D isothermal Bingham lava flow as initial flow conditions, and then impose Martian, Venusian, and terrestrial (submarine and subaerial) cooling environments and compare the cooling and flow rates for the different environments and flow rheologies.

Points of Contact

Susan Sakimoto
Universities Space Research Association
NASA Goddard Space Flight Center
sakimoto@denali.gsfc.nasa.gov
301-286-2691

Anil Deane
University of Maryland
deane@ipst.umd.edu
301-405-4866
and
NASA Goddard Space Flight Center
deane@laplace.gsfc.nasa.gov
301-286-7803