Giordano Tierra Chica

Previous Scheduled Teaching

Published Intellectual Contributions

Conference Proceeding

• Tierra Chica, G., Guillen-Gonzalez, F., Rodriguez-Bellido, M.A. (2018). Splitting Schemes for Mixtures of Nematic-Isotropic Flows with Anchoring Effects. 10665 77-84. International Conference on Large-Scale Scientific Computing LSSC 2017, Lecture Notes in Computer Science.
• Tierra Chica, G., Rodriguez-Bellido, M.A., Guillen-Gonzalez, F. (2015). Linear stable splitting schemes for a mixture of newtonian and nematic fluids with anchoring effects. 833-838. Proceedings of the XXIV Congress on Differential Equations and Applications / XIV Congress on Applied Mathematics.
• Tierra Chica, G., Malek, J. (2015). Numerical approximations for unsteady flows of incompressible fluids characterized by non-monotone implicit constitutive relations. 797-802. Proceedings of the XXIV Congress on Differential Equations and Applications / XIV Congress on Applied Mathematics.
• Tierra Chica, G., Guillen-Gonzalez, F. (2012). Efficient numerical approximations of the Cahn-Hilliard diffuse interface model. (paper 53) Proceedings of the First ECCOMAS Young Investigators Conference on Computational Methods in Applied Sciences.

Journal Article

• Guillen-Gonzalez, F., Tierra Chica, G. (2024). Structure preserving numerical schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility. Computers & Mathematics with Applications. 172 181-201.
• Guillen-Gonzalez, F., Tierra Chica, G. (2024). Energy-stable and boundedness preserving numerical schemes for the Cahn-Hilliard equation with degenerate mobility. Applied Numerical Mathematics. 196 62-82.
• Guillen-Gonzalez, F., Tierra Chica, G. (2024). Finite Element numerical schemes for a chemo-attraction and consumption model. Journal of Computational and Applied Mathematics. 441 115676.
• Swain, J., Tierra Chica, G. (2024). Linear Numerical Schemes for a Q-Tensor System for Nematic Liquid Crystals. Computer Methods in Applied Mechanics and Engineering. 430 (117190) 26. https://www.sciencedirect.com/science/article/pii/S0045782524004468?via%3Dihub
• Pawale, T., Hashemi, S., Swain, J.D., Tierra Chica, G., Li, X. (2023). Directed stabilization and annihilation of defects in nematic phase of liquid crystal by chemically patterned surfaces. Advanced Materials Interfaces. 10 (2300136)
• El-Haddad, M., Tierra Chica, G. (2022). A thermodynamically consistent model for two-phase incompressible flows with different densities. Derivation and energy-stable numerical schemes. Computer Methods in Applied Mechanics and Engineering. 389 114328.
• Guillen-Gonzalez, F., Rodriguez-Bellido, M., Tierra Chica, G. (2021). Fluid vesicles with internal nematic order. Physica D: Nonlinear Phenomena. 415 132768. https://www.sciencedirect.com/science/article/pii/S0167278920301871
• Guillen-Gonzalez, F., Rodriguez-Bellido, M., Tierra Chica, G. (2020). Nematic order on a deformable vesicle with anchoring effects. Results in Applied Mathematics. 8 100102.
• Tierra Chica, G., Strasser, P., Lukacova-Medvidova, M., Dunweg, B. (2019). Energy-stable linear schemes for polymer-solvent phase field models. Computers & Mathematics with Applications. 77 125-143.
• Tierra Chica, G., Janecka, A., Malek, J., Prusa, V. (2019). Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor. Acta Mechanica. 230 729-747.
• Tierra Chica, G., Camaño, J., Oyarzua, R., Ruiz-Baier, R. (2018). Error analysis of an augmented mixed method for the Navier-Stokes problem with mixed boundary conditions. IMA Journal of Numerical Analysis. 38 1452-1484.
• Tierra Chica, G., Guillen-Gonzalez, F. (2018). Unconditionally energy stable numerical schemes for phase-field vesicle membrane model. Journal of Computational Physics. 354 67-85.
• Tierra Chica, G., Camaño, J., Oyarzua, R. (2017). Analysis of an augmented mixed-FEM for the Navier-Stokes problem. Mathematics of Computation. 86 589-615.
• Tierra Chica, G., Gatica, G., Ruiz-Baier, R. (2016). A mixed finite element method for Darcy’s equations with pressure dependent porosity. Mathematics of Computation. 85 1-33.
• Tierra Chica, G., Gatica, G., Ruiz-Baier, R. (2016). A posteriori error analysis of an augmented mixed method for the Navier-Stokes equations with nonlinear viscosity. Computers & Mathematics with Applications. 72 2289-2310.
• Tierra Chica, G., Camaño, J., Gatica, G., Oyarzua, R. (2016). An augmented mixed finite element method for the Navier-Stokes equations with variable viscosity. SIAM Journal on Numerical Analysis. 54 1069-1092.
• Tierra Chica, G., Guillen-Gonzalez, , F., Rodriguez-Bellido, M.A. (2016). Linear unconditional energy-stable splitting schemes for a phase-field model for Nematic-Isotropic flows with anchoring effects. International Journal for Numerical Methods in Engineering. 108 535-567.
• Tierra Chica, G., Guillen-Gonzalez, F. (2015). Approximation of Smectic-A liquid crystals. Computer Methods in Applied Mechanics and Engineering. 290 342-361.
• Tierra Chica, G., Pavissich, J.P., Nerenberg, R., Xu, Z., Alber, M.S. (2015). Multicomponent model of deformation and detachment of a biofilm under fluid flow. Journal of The Royal Society Interface. 12 20150045.
• Tierra Chica, G., Guillen-Gonzalez, F. (2015). Numerical methods for solving the Cahn-Hilliard equation and its applicability to related Energy-based models. Archives of Computational Methods in Engineering. 22 269-289.
• Tierra Chica, G., Bonnivard, M., Suarez-Grau, F.J. (2014). Influence of wavy riblets on the slip behavior of viscous fluids. Zeitschrift für angewandte Mathematik und Physik. 67 (27)
• Tierra Chica, G., Guillen-Gonzalez, F. (2014). Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models. Computers & Mathematics with Applications. 68 821-846.
• Tierra Chica, G., Guillen-Gonzalez, F. (2014). Splitting Schemes for a Navier-Stokes-Cahn-Hilliard Problem Modeling Two-Fluids with Different Densities. Journal of Computational Mathematics. 32 643-664.
• Tierra Chica, G., Shrout, J.D., Alber, M., Driscoll, C.M., Morales-Soto, N., Harvey, C.W., Amiri, A., Anyan, M.E. (2014). Type IV Pili Interactions Promote Intercellular Association and Moderate Swarming of Pseu.. PNAS: Proceedings of the National Academy of Sciences. 111 18013-18018.
• Tierra Chica, G., Guillen-Gonzalez, F. (2013). On linear schemes for a Cahn Hilliard Diffuse Interface Model. Journal of Computational Physics. 234 140-171.
• Tierra Chica, G., Guillen-Gonzalez, F. (2012). Superconvergence in velocity and pressure for the 3D Navier-Stokes. SeMA Journal. 57 49-67.

Contracts, Grants and Sponsored Research

Fellowship

• Tierra Chica, G., "Creative and Research Enhancement Activity Time for Engagement program (CREATE)," University of North Texas, $4000 Funded. (2024 - 2024).
• Tierra Chica, G., "Numerical PDEs: Analysis, Algorithms, and Data Challenges," sponsored by The Institute for Computational and Experimental Research in Mathematics (ICERM), Federal, Funded. (2024 - 2024).

Grant - Research

• Tierra Chica, G., "Accurate and Efficient Numerical Methods for Energy-Based Systems," sponsored by Simons Foundation, Private, $42000 Funded. (2024 - 2029).
• Li, X., Tierra Chica, G., "Investigation of structure-function relationships for improving ion transport in liquid crystal-based ion transport devices using thin-film directed self-assembly," sponsored by Division of Research and Innovation, University of North Texas, $9770 Funded. (2023 - 2023).