Final Report Summary - MAMMA (magma ascent mathematical modelling and analysis)
The main goal of the MAMMA project was to understand, through physical and mathematical models, how conduit processes control volcanic unrest and eruption characteristics. The project has been based on collaboration between the School of Earth and Space Exploration of the Arizona State University (United States), home of a vibrant volcanology and planetary science community, and the Italian Istituto Nazionale di Geofisica e Vulcanologia, the largest European body dealing with research in geophysics and volcanology. As such, the proposed work was focused on the mathematical modelling of complex volcanic systems, and intended to develop novel techniques for the computation and analysis of multi-physics models in that the codes developed will solve the fully coupled magma and gas flow and the changes in rheology associated with the degassing and crystallisation processes. To achieve the stated goals, the researcher developed fast and scalable numerical finite-volume models for multi-physics coupled problems, in both Fortran 90 and C++ within the OpenFOAM framework. By the end of the project the numerical solver was extended to two / three dimensional (2D / 3D) and parallelised to run on a High-performance computer (HPC) cluster.
With particular regards to the outgoing phase, a primary goal was to critically evaluate the conceptual model and numerical results with quantitative information on eruptive physical parameters acquired from laboratory experiments, petrologic analysis and eruptive products collected in field trips, under the guidance of the outgoing supervisor. An additional goal of the outgoing phase was to interact with planetary scientists with expertise in Mars and Lunar geology and volcanology, in order to understand the role of gravity in controlling conduit geometry on Mars and the Earth's moon, and transitions between effusive and explosive eruptions under Martian and Lunar conditions, where gravity and atmospheric pressure are significantly lower than on Earth. The first part of the outgoing phase was devoted to the analysis of the applicability of existing models to effusive and explosive eruptions. The analysis of existing models led to the necessity to find a new formulation for the equations of a multiphase flow, able to deal with full range of gas phase volume fraction (from absence of gas to very high gas fractions) and the complex two-way relationships between magma degassing, crystallisation characteristics and magma ascent dynamics. The extension of the theory of thermodynamically compatible systems to a magmatic system, and the development of new finite-volume numerical schemes, allowed to define a new model and a solution scheme able to describe the transition from homogeneous magma to a gas-particle dispersion and to simulate magma ascent through the conduit in both effusive and explosive eruptions. During the outgoing phase a 1D steady version of the model has been implemented in a new code and the results have been presented in an invited talk at the American Geophysical Union (AGU) Fall Meeting 2011.
As concerns the return phase, a primary goal was to complete the new formulation for the equations of multiphase flows, able to deal with full range of gas phase volume fraction (from absence of gas to very high gas fractions) and the complex two-way relationships between magma degassing, crystallisation characteristics and magma ascent dynamics. The 1D steady version of the model, developed during the outgoing phase, has been extended to the transient case and a 2D / 3D model of a simplified version of the model has been developed within the open source computational fluid dynamic (CFD) software package OpenFOAM. The numerical framework developed has the advantage that it is not tied to the particular choice of transport or constitutive equations, but rather, it is tied to the conservative form of the equation, which allows easy changes to the different constitutive terms - including, for example, viscosity models, solubility laws, drag terms, lateral degassing - without the need to modify the numerical solver. The model has been validated for several test-cases, in order to verify the capability of the solver to properly solve for shock and rarefaction waves in multiphase flows.
As regards to the constitutive equations, during the return phase some time has been spent for the implementation in the code of proper models for the fragmentation process and the disequilibium crystallisation and degassing. To date, the influence of the fragmentation process on the dynamics of the gas-particle regime has been largely neglected. In order to better understand the role of the fragmentation process in explosive events the fellow has started a new collaboration with the Department of Earth and Environmental Sciences at the Ludwig-Maximilians-University (LMU) in Munich, Germany. Different fragmentation criterion for highly viscous bubbly magmas estimated from shock tube experiments at LMU has been implemented in the code and several test cases has been selected for the comparison between laboratory experiments and the numerical results of the model. As regards to the implementation of disequilibium crystallisation and degassing in the code, recent numerical models have contributed to investigate the influence of different parameters on decompression dynamics during extrusive and explosive eruption regimes, but the lack of consideration of feedback effects, in particular of the decompression path on the crystal growth and gas exsolution, limits the applicability of such models to extremely low ascent rate eruptions, when equilibirum can be assumed, or to very high ascent rate eruptions in which the changes in crystal content and exsolution effects are relatively small and can be neglected. The new formulation of the model allows to account for disequilibrium crystallisation and degassing and the results have been validated with laboratory decompression experiments.
In order to use real-time volcano monitoring data to interpret subsurface dynamics and predict future eruptive activity the sensitivity of forward model outcomes to uncertain or variable input parameters and processes must be assessed and corresponding uncertainty quantified systematically. In response to this issue, we extended the sensitivity studies developed during the outgoing phase and the new model has been now interfaced with the Design analysis kit for optimisation and terra-scale applications (DAKOTA) toolkit, allowing effective and realistic comparisons between outcomes of the model and data. Uncertainty quantification and sensitivity analysis results obtained for several well-documented periods of the ongoing eruption of the Soufrière Hills volcano has been presented at the American Geophysical Union (AGU) Fall Meeting 2012.
The results obtained during the return phase of the project not only will contribute to the competitiveness and excellence of the European Union (EU) in volcanological research and risk assessment, but they will also serve as a base to create a mutually beneficial co-operation between Europe and United States. The codes developed by the researcher during the return phase are actually used by Doctor of Philosophy (PhD) students in both the outgoing and return hosts, and this will strengthen the collaboration between them. Furthermore, the applications to planetary volcanism will open new research fields and perspective for the return host organisation and will enhance the scientific excellence of the EU.
With particular regards to the outgoing phase, a primary goal was to critically evaluate the conceptual model and numerical results with quantitative information on eruptive physical parameters acquired from laboratory experiments, petrologic analysis and eruptive products collected in field trips, under the guidance of the outgoing supervisor. An additional goal of the outgoing phase was to interact with planetary scientists with expertise in Mars and Lunar geology and volcanology, in order to understand the role of gravity in controlling conduit geometry on Mars and the Earth's moon, and transitions between effusive and explosive eruptions under Martian and Lunar conditions, where gravity and atmospheric pressure are significantly lower than on Earth. The first part of the outgoing phase was devoted to the analysis of the applicability of existing models to effusive and explosive eruptions. The analysis of existing models led to the necessity to find a new formulation for the equations of a multiphase flow, able to deal with full range of gas phase volume fraction (from absence of gas to very high gas fractions) and the complex two-way relationships between magma degassing, crystallisation characteristics and magma ascent dynamics. The extension of the theory of thermodynamically compatible systems to a magmatic system, and the development of new finite-volume numerical schemes, allowed to define a new model and a solution scheme able to describe the transition from homogeneous magma to a gas-particle dispersion and to simulate magma ascent through the conduit in both effusive and explosive eruptions. During the outgoing phase a 1D steady version of the model has been implemented in a new code and the results have been presented in an invited talk at the American Geophysical Union (AGU) Fall Meeting 2011.
As concerns the return phase, a primary goal was to complete the new formulation for the equations of multiphase flows, able to deal with full range of gas phase volume fraction (from absence of gas to very high gas fractions) and the complex two-way relationships between magma degassing, crystallisation characteristics and magma ascent dynamics. The 1D steady version of the model, developed during the outgoing phase, has been extended to the transient case and a 2D / 3D model of a simplified version of the model has been developed within the open source computational fluid dynamic (CFD) software package OpenFOAM. The numerical framework developed has the advantage that it is not tied to the particular choice of transport or constitutive equations, but rather, it is tied to the conservative form of the equation, which allows easy changes to the different constitutive terms - including, for example, viscosity models, solubility laws, drag terms, lateral degassing - without the need to modify the numerical solver. The model has been validated for several test-cases, in order to verify the capability of the solver to properly solve for shock and rarefaction waves in multiphase flows.
As regards to the constitutive equations, during the return phase some time has been spent for the implementation in the code of proper models for the fragmentation process and the disequilibium crystallisation and degassing. To date, the influence of the fragmentation process on the dynamics of the gas-particle regime has been largely neglected. In order to better understand the role of the fragmentation process in explosive events the fellow has started a new collaboration with the Department of Earth and Environmental Sciences at the Ludwig-Maximilians-University (LMU) in Munich, Germany. Different fragmentation criterion for highly viscous bubbly magmas estimated from shock tube experiments at LMU has been implemented in the code and several test cases has been selected for the comparison between laboratory experiments and the numerical results of the model. As regards to the implementation of disequilibium crystallisation and degassing in the code, recent numerical models have contributed to investigate the influence of different parameters on decompression dynamics during extrusive and explosive eruption regimes, but the lack of consideration of feedback effects, in particular of the decompression path on the crystal growth and gas exsolution, limits the applicability of such models to extremely low ascent rate eruptions, when equilibirum can be assumed, or to very high ascent rate eruptions in which the changes in crystal content and exsolution effects are relatively small and can be neglected. The new formulation of the model allows to account for disequilibrium crystallisation and degassing and the results have been validated with laboratory decompression experiments.
In order to use real-time volcano monitoring data to interpret subsurface dynamics and predict future eruptive activity the sensitivity of forward model outcomes to uncertain or variable input parameters and processes must be assessed and corresponding uncertainty quantified systematically. In response to this issue, we extended the sensitivity studies developed during the outgoing phase and the new model has been now interfaced with the Design analysis kit for optimisation and terra-scale applications (DAKOTA) toolkit, allowing effective and realistic comparisons between outcomes of the model and data. Uncertainty quantification and sensitivity analysis results obtained for several well-documented periods of the ongoing eruption of the Soufrière Hills volcano has been presented at the American Geophysical Union (AGU) Fall Meeting 2012.
The results obtained during the return phase of the project not only will contribute to the competitiveness and excellence of the European Union (EU) in volcanological research and risk assessment, but they will also serve as a base to create a mutually beneficial co-operation between Europe and United States. The codes developed by the researcher during the return phase are actually used by Doctor of Philosophy (PhD) students in both the outgoing and return hosts, and this will strengthen the collaboration between them. Furthermore, the applications to planetary volcanism will open new research fields and perspective for the return host organisation and will enhance the scientific excellence of the EU.