Computational fluid dynamics

High-resolution finite difference and spectral methods for porous media flow

Flow instabilities are a central research topic in our group. Modeling unstable flow requires high-resolution simulations that can capture the rich structures and patterns that ensue. I develop high-order finite difference and spectral methods that allow very accurate and efficient simulation schemes. We apply these algorithms to model gravitational and viscous instabilities. We use these simulations to understand the key physical mechanisms at play, as well as their scaling properties.

Numerical methods for fourth-order PDEs

A fundamental challenge in our physics-oriented simulation tools is the development of numerical schemes for higher-order PDEs, in particular phase-field models that include fourth-order terms. We use a variety of techniques, from finite differences and spectral methods to finite volumes and isogeometric analysis, but this is an emerging research topic with huge opportunities and many open questions.

High-order finite volume schemes with meshfree reconstruction

Many of the nice approximation properties of finite difference and spectral methods are linked to the structured nature of their associated computational grids. It is challenging to develop high-order methods for unstructured grids, in particular for conservation laws. I developed finite volume methods based on moving least-square reconstruction. These schemes retain the robustness and physical interpretation of finite volume methods, and allow for higher-order accuracy.

Selected Publications

1. Pattern formation and coarsening dynamics in three-dimensional convective mixing in porous media.
   X. Fu, L. Cueto-Felgueroso, and R. Juanes, Philosophical Transactions of the Royal Society A, accepted, in press.

2. Synergetic fluid mixing from viscous fingering and alternating injection.
   B. Jha, L. Cueto-Felgueroso, and R. Juanes, Physical Review Letters, 111, 144501 (2013), doi:10.1103/PhysRevLett.111.144501. (pdf; Videos)

3. Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium.
   H. Gomez, L. Cueto-Felgueroso, and R. Juanes, Journal of Computational Physics, 238, 217-239 (2013), doi:10.1016/j.jcp.2012.12.018

4. Fluid mixing from viscous fingering.
   B. Jha, L. Cueto-Felgueroso and R. Juanes, Physical Review Letters, 106(19), 194502 (2011), doi:10.1103/PhysRevLett.106.194502

5. Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems.
   L. Cueto-Felgueroso and R. Juanes, Journal of Computational Physics, 228:6536-6552 (2009), doi:10.1016/j.jcp.2009.05.045

6. A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations.
   L. Cueto-Felgueroso and J. Peraire, Journal of Computational Physics, 227:9985-10017 (2009)

7. A new shock-capturing technique based on Moving Least Squares for higher-order numerical schemes on unstructured grids.
   X. Nogueira, L. Cueto-Felgueroso, I. Colominas, F. Navarrina and M. Casteleiro, Computer Methods in Applied Mechanics and Engineering, 199: 2544–2558 (2010)

8. Implicit Large Eddy Simulation of non-wall-bounded turbulent flows based on the multiscale properties of a high-order finite volume method.
   X. Nogueira, L. Cueto-Felgueroso et al., Computer Methods in Applied Mechanics and Engineering, 199:615–624 (2010)

9. On the accuracy of finite volume and discontinuous Galerkin discretizations for compressible flow on unstructured grids.
   X. Nogueira, L. Cueto-Felgueroso et al., International Journal for Numerical Methods in Engineering, 78:1553-1584 (2009)

10. High-order finite volume methods and multiresolution reproducing kernels.
    L. Cueto-Felgueroso and I. Colominas, Archives of Computational Methods in Engineering, 15:185-228 (2008)

11. Finite volume solvers and Moving Least-Squares approximations for the compressible Navier-Stokes equations on unstructured grids.
    L. Cueto-Felgueroso et al., Computer Methods in Applied Mechanics and Engineering, 196:4712-4736 (2007)

12. High-order finite volume schemes on unstructured grids using moving least-squares reconstruction. Application to shallow water dynamics.
    L. Cueto-Felgueroso et al., International Journal for Numerical Methods in Engineering, 65:295-331 (2006)

13. On the Galerkin formulation of the smoothed particle hydrodynamics method.
    L. Cueto-Felgueroso et al., International Journal for Numerical Methods in Engineering, 60:1475-1512 (2004)