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Coloured pencils breaking the surface of water, photographed at the instant of impact.

Photograph by Alejandro Cisneros

Pablo
Castañeda

Portrait of Pablo Castañeda.

I study how a discontinuity propagates in conservation laws, and its application to fluid flow in porous media and to transport phenomena.

Full professor, Department of Mathematics, ITAM. Member of Mexico's National System of Researchers (SNII, formerly SNI), Level I since 2015.

From 1 August 2026 to 31 July 2027 I am on unpaid leave, living in Brazil and working on scientific advisory and collaboration projects.

13years at ITAM

6theses supervised

28published works

The Riemann problem

One fluid enters a reservoir and meets another. At the point of contact there is a jump, and the question is what happens next: that jump opens into a fan of waves that can be computed. My work is to find those solutions and to show that, across very different permeability models, they all share the same structure.

Saturation triangle with a solution of the Riemann problem A triangle whose vertices are the three phases: water at the top, gas at the bottom left and oil at the bottom right. From the initial state a rarefaction curve runs to an intermediate state, and from there a straight segment, which is a shock, to the final state. water gas oil
In yellow the rarefaction, where the solution varies continuously. In orange the shock: there the solution jumps.
Tenochtitlan on its lake, mounted as a frame of 35 mm film.
Tenochtitlan. From the roll Hyperbolica 1, frames 5 and 6.

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