Abstract
In this chapter, we present an application of the variational data assimilation method to the problem for determination of thermal and dynamic characteristics of lava flow from thermal measurements at lava’s upper surface. Assuming that the temperature and the heat flow are known at the lava’s upper surface, the missing condition at the lower surface of the lava is determined at first, and then the flow characteristics (temperature and flow velocity) are resolved in the entire model domain.
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References
Costa A, Macedonio G (2005a) Computational modeling of lava flows: a review. In: Manga M, Ventura G (eds) Kinematics and dynamics of lava flows. Geological Society of America Special Papers 396, Boulder, pp 209–218
Costa A, Macedonio G (2005b) Numerical simulation of lava flows based on depth-averaged equations. Geophys Res Lett 32:L05304. doi:10.1029/2004GL021817
Cutter S, Ismail-Zadeh A, Alcántara-Ayala I, Altan O, Baker DN, Briceño S, Gupta H, Holloway A, Johnston D, McBean GA, Ogawa Y, Paton D, Porio E, Silbereisen RK, Takeuchi K, Valsecchi GB, Vogel C, Wu G (2015) Pool knowledge to stem losses from disasters. Nature 522:277–279
Fletscher R (2000) Practical methods of optimization, 2nd edn. Wiley, Chichester
Flynn LP, Harris AJL, Wright R (2001) Improved identification of volcanic features using Landsat 7 ETM+. Remote Sens Environ 78:180–193
Griffiths RW (2000) The dynamics of lava flows. Annu Rev Fluid Mech 32:477–518
Harris AJL, Flynn LP, Matias O, Rose WI, Cornejo J (2004) The evolution of an active silicic lava flow field: an ETM+ perspective. J Volcanol Geotherm Res 135:147–168
Harris AJL, Dehn J, Calvari S (2007) Lava effusion rate definition and measurement: a review. Bull Volcanol 70:1–22
Hidaka M, Goto A, Umino S, Fujita E (2005) VTFS project: development of the lava flow simulation code LavaSIM with a model for three-dimensional convection, spreading, and solidification. Geochem Geophys Geosyst 6:Q07008. doi:10.1029/2004GC000869
Ishihara K, Iguchi M, Kamo K (1989) Numerical simulation of lava flows on some volcanoes in Japan. In: Fink J (ed) Lava flows and domes, vol 2, IAVCEI Proc. Volcanol. Springer, New York
Ismail-Zadeh A, Tackley P (2010) Computational methods for geodynamics. Cambridge University Press, Cambridge
Ismail-Zadeh A, Korotkii A, Schubert G, Tsepelev I (2007) Quasi-reversibility method for data assimilation in models of mantle dynamics. Geophys J Int 170:1381–1398
Kabanikhin SI (2011) Inverse and ill-posed problems. Theory and applications. De Gruyter, Berlin
Korotkii AI, Kovtunov DA (2006) Reconstruction of boundary regimes in an inverse problem of thermal convection of a high viscous fluid. Proc Inst Math Mech Ural Branch Russ Acad Sci 12(2):88–97 (in Russian)
Korotkii AI, Starodubtseva YV (2014) Direct and inverse problems for models of stationary reactive-convective-diffusive flow. Proc Inst Math Mech Ural Branch Russ Acad Sci 20(3):98–113 (in Russian)
Korotkii A, Kovtunov D, Ismail-Zadeh A, Tsepelev I, Melnik O (2016) Quantitative reconstruction of thermal and dynamic characteristics of lava flow from surface thermal measurements. Geophys J Int. doi:10.1093/gji/ggw117
Ladyzhenskaya OA (1969) The mathematical theory of viscous incompressible flow. Gordon and Breach, New York
Lions JL (1971) Optimal control of systems governed by partial differential equations. Springer, Berlin/Heidelberg
Miyamoto H, Sasaki S (1998) Numerical simulations of flood basalt lava flows: roles of parameters on lava flow morphologies. J Geophys Res 103:27489–27502
Neri A (1998) A local heat transfer analysis of lava cooling in the atmosphere: application to thermal diffusion-dominated lava flows. J Volcanol Geotherm Res 81:215–243
Nocedal J, Wright SJ (1999) Numerical optimization. Springer, New York
Patankar SV, Spalding DB (1972) A calculation procedure for heat and mass transfer in three-dimensional parabolic flows. Int J Heat Mass Transf 15:1787–1806
Polak E (1997) Optimization: algorithms and consistent approximations. Springer, Berlin/Heidelberg
Short NM, Stuart LM (1983) The heat capacity mapping mission (HCMM) anthology. Scientific and Technical Information Branch, National Aeronautics & Space Administration, Washington, DC
Sweby PK (1984) High resolution schemes using flux limiters for hyperbolic conservation laws. J Numer Anal 21:995–1011
Temam R (1977) Navier-Stokes equations: theory and numerical analysis. North-Holland, Amsterdam
Tikhonov AN, Arsenin VY (1977) Solution of ill-posed problems. Winston, Washington, DC
Tsepelev I, Ismail-Zadeh A, Melnik O, Korotkii A (2016) Numerical modelling of fluid flow with rafts: an application to lava flows. J Geodyn. doi:10.1016/j.jog.2016.02.010
Van der Vorst HA (1992) BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comput 13(2):631–644
Wang Y, Hutter K (2001) Comparison of numerical methods with respect to convectively dominated problems. Int J Numer Methods Fluids 37:721–745
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Ismail-Zadeh, A., Korotkii, A., Tsepelev, I. (2016). Application of the Variational Method to Lava Flow Modelling. In: Data-Driven Numerical Modelling in Geodynamics: Methods and Applications. SpringerBriefs in Earth Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-27801-8_4
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DOI: https://doi.org/10.1007/978-3-319-27801-8_4
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