Research
My research activity is focused on Computational and Applied Mathematics.
My research interests include the design, implementation and numerical analysis of new and effective computational techniques for solving scientific or engineering problems.
I am interest in cooperation with pure mathematicians, applied mathematicians, numerical analysts, computational scientists as well as engineers to developed and improve analysis of existing methods and algorithms is of importance, including the effectiveness and applicability illustrated by nontrivial numerical examples.
My research interests include theory, modeling, numerical methods for differential equations and simulation of multiscale multiphysics complex systems. Such nonlinear models appear naturally in basic and applied sciences related to energy, climate, water, agriculture and they are also current events for a green world. Numerical methods for differential equations and simulation of multiscale multiphysics complex systems have a huge impact in the study of petroleum reservoir located in the pre-salt area in marine coast of Brazil.
Today, Brazil span collaborations across the globe, from North and South America to Europe and the Asia-Pacific region, which in turn include many of the worlds most advanced countries but also emerging countries. Together with my group at IMECC-UNICAMP, our goal is to build a stronger, cleaner, fairer world to good the development of high level Industrial and Applied Mathematics linked to emerging and crucial issues as such environment and climate change challenging linked to sustainable infrastructure and energy efficiency.
My research is focused on the numerical simulation of realistic models as such hyperbolic problems and balance laws on the foundations of mathematical modeling and numerical simulation to the study of fluid dynamics in porous media.
Current research topics:
- Numerical Analysis via Weak Asymptotic Methods.
- Numerical Methods for Balance Laws and Hyperbolic Systems of Conservations Laws.
- Flow in Porous Media and Hydrodynamic Models.
- Positive Lagrangian-Eulerian Schemes for Multidimensional Systems of Hyperbolic Conservation Laws.
- Convergence analysis of Generalized Multiscale Finite Element Methods.
- Implementation (by using MPI) of Mixed Finite Element and Recursive Mixed Multiscale for Karst Conduit-Flow in Carbonate Reservoirs.
- Computational Fluid Dynamics and nonlinear transport phenomena, as such, relativistic magnetohydrodynamics equations, 3D vorticity equation, Orszag-Tang vortex system, vortex sheet models, vortex street problems, flow in porous media, dynamics of the interface between two fluids, and 2D quasi-geostrophic equations, isentropic system of gas dynamics, shallow water equations with discontinuous bathymetry among others nontrivial multidimensional systems.
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