Research
My research interest is the development and analysis of new numerical schemes for solving partial differential equations, which model most industrial and environmental problems. The activities that I mainly focus on are:
singularly perturbed parabolic–elliptic problems,
scalar–transport and Navier–Stokes equations,
high–order discretization techniques within finite difference, finite volume, and discontinuous Galerkin family.
Other topics that I have been dealing with or also interest me are the following:
computational fluid dynamics,
computational magnetohydrodynamics,
turbulence models,
numerical integration,
Lie group method.
Below you find a list of my publications, conferences, and projects.
Publications
In progess
Llorente, V.J.,: Limiting of order of accuracy by machine epsilon.
Under Review
Llorente, V.J., Padilla, E.M., Díez-Minguito, M., and Valle-Levinson, A.: Conserved Quantities in the Ocean Surface Boundary Layer: A fresh perspective on a classical problem (Submitted to Geophysical Research Letters)
Articles in peer-review journals
2024
Llorente, V.J. (2024). Theoretical considerations of the volume penalization immersed boundary method for turbulent flows. Physics of Fluids 36(7), Article XXXXXX. doi: 10.1063/5.0213290.
Llorente, V.J., Padilla, E.M., and Díez-Minguito, M. (2024). Sensitivity of boundary layer features to depth-dependent baroclinic pressure gradient and turbulent mixing in an ocean of finite depth. Ocean Modelling 189, Article 102359. doi: 10.1016/j.ocemod.2024.102359
2023
Llorente, V.J., Kou, J., Valero, E., and Ferrer, E. (2023): A modified equation analysis for immersed boundary methods based on volume penalization: applications to linear advection-diffusion and high-order discontinuous Galerkin schemes. Computers & Fluids 257, Article 105869. doi: 10.1016/j.compfluid.2023.105869
Llorente, V.J., and Pascau, A. (2023). Extension of an exponential discretization scheme to multidimensional convection-diffusion problems. Computers & Fluids 251, Article 105740. doi: 10.1016/j.compfluid.2022.105740
2020
Llorente, V.J., ten Thije Boonkkamp, J.H.M., Pascau, A., and Anthonissen, M.J.H. (2020). Similarities and differences of two exponential schemes for convection-diffusion problems: The FV-CF and ENATE scheme. Applied Mathematics and Computation 365, Article 124700. doi: 10.1016/j.amc.2019.124700
Llorente, V.J., and Pascau, A. (2020). Compact Integration Rules as a quadrature method with some applications. Computers & Mathematics with Applications 79(5), 1241 – 1265. doi: 10.1016/j.camwa.2019.08.038
2019
Llorente, V.J., and Pascau, A. (2019). Numerical simulations of magnetorheological fluids flowing between two fixed parallel plates. Applied Mathematical Modelling 74, 151 – 169. doi: 10.1016/j.apm.2019.04.047
2016
Llorente, V., Rubio, G., Pascau, A., Ferrer, E., and Arici, M. (2016). Comparison of the ENATE approach and discontinuous Galerkin spectral element method in 1D nonlinear transport equations. Computers Assisted Methods in Engineering and Science 23, 133 – 146. [pdf]
Conference papers
2022
Llorente, V.J., Padilla, E.M., and Díez-Minguito, M. (2022). High-order numerical sensitivity tests of wind-driven boundary layer currents to finite depth, inhomogeneous eddy viscosity, and baroclinic pressure gradient. In: M. Ortega-Sánchez (Ed.), Proceedings of 39th IAHR World Congress (pp. 4730 – 4735). IAHR. doi: 10.3850/IAHR-39WC2521716X20221208
Llorente, V.J., Lodares, D., Ferrer, E., and Valero, E. (2022). An Immersed Boundary Method for the CFD Solver Airbus-CODA. In: ECCOMAS 2022, Proceedings of the 8th European Congress on Computational Methods in Applied Sciences and Engineering (pp. 1 – 12). ECCOMAS. doi: 10.23967/eccomas.2022.047
2016
Pascau, A., Arici, M., and Llorente, V. (2016). ENATE procedure for the Navier-Stokes equations. In ICCFD 2016, Proceedings of 9th International Conference on Computational Fluid Dynamics (pp. 1 – 9). ICCFD. [pdf]
Conferences
Conference presentations (speaker underlined)
2024
Cabellero-Martínez, O.A., Díez-Minguito, M., and Llorente, V.J. (2024, May 15 – 17). Modos propios de oscilación de Puerto Foster (Isla Decepción, Antártida) [Poster presentation]. X Simposio de estudios polares, Salamanca, Spain.
2023
Llorente, V.J., Padilla E.M., and Díez-Minguito, M. (2023, April 23 – 28). Conserved quantities in the Ekman layer [Oral presentation]. EGU General Assembly 2023, Vienna, Austria. doi: 10.5194/egusphere-egu23-8914
2022
Llorente, V.J., Padilla E.M., and Díez-Minguito, M. (2022, June 19 – 24). High-order numerical sensitivity tests of wind-driven boundary layer currents to finite depth, inhomogeneous eddy viscosity, and baroclinic pressure gradient [Oral presentation]. 39th IAHR World Congress 2022: From Snow to Sea, Granada, Spain.
Llorente, V.J., Lodares, D., Ferrer, E., and Valero E. (2022, June 5 – 9). An Immersed Boundary Method for the CFD Solver Airbus-CODA [Oral presentation]. The 8th European Congress on Computational Methods in Applied Sciences and Engineering, Oslo, Norway.
Llorente, V.J. (2022, January 17 – 21). Lie symmetry reductions of a transport equation under stream-function coordinates [Poster presentation]. Congreso Bienal de la Real Sociedad Matemática Española, Ciudad Real, Spain.
2021
Llorente, V.J., and Pascau, A. (2021, January 11 – 15). ENATE, a High-Order Scheme for Complex Flows [Virtual presentation]. 14th World Congress in Computational Mechanics and ECCOMAS Congress, Paris, France.
2019
Llorente, V.J., and Pascau, A. (2019, September 30 – October 4). ENATE for complex domains II. Von Newmann and Robin boundary conditions [Oral presentation]. European Numerical Mathematics and Advanced Applications Conference, Egmondaan Zee, The Netherlands.
Llorente, V.J., and Pascau, A. (2019, September 30 – October 4). ENATE for complex domains I. Dirichlet boundary conditions [Oral presentation]. European Numerical Mathematics and Advanced Applications Conference, Egmondaan Zee, The Netherlands.
Llorente, V.J., and Pascau, A. (2019, September 11 – 14). ENATE, a high-order scheme for transport equations [Oral presentation]. 22nd Congress on Thermal Science and Technology, Kocaeli, Turkey.
Llorente, V.J., and Pascau, A. (2019, July 15 – 19). The ENATE approach for steady incompressible Navier-Stokes (NS) equations [Oral presentation]. International Congress on Industrial and Applied Mathematics, Valence, Spain.
Pascau, A., and Llorente, V.J. (2019, July 15 – 19). ENATE, a highly parallelizable scheme for transport equations [Oral presentation]. International Congress on Industrial and Applied Mathematics, Valence, Spain.
Llorente, V.J., and Pascau, A. (2019, July 1 – 3). High-order ENATE for transport problems [Oral and Poster presentation]. Congress on Numerical Methods in Engineering, Guimarães, Portugal.
Llorente, V.J. (2019, June 25 – 27). Desarrollo de una aproximación numérica de alto orden para la simulación en mecánica de fluidos [Oral presentation]. Jornadas de Investigadores en Formación: Fomentando la Interdisciplinariedad, Granada, Spain.
Llorente, V.J., and Pascau, A. (2019, June 17 – 20). The ENATE scheme for Shallow Water (SW) simulations [Oral presentation]. Modelling Hydrodynamics for Water Resources, Zaragoza, Spain.
Llorente, V.J., and Pascau, A. (2019, April 1 – 5). ENATE, a high-order scheme for convection-diffusion problems [Oral presentation]. European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications, Madrid, Spain.
Llorente, V.J., and Pascau, A. (2019, April 1 – 5). ENATE, a high-order scheme for Cartesian grids with arbitrary expansion/contraction ratios [Oral presentation]. European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications, Madrid, Spain.
2017
Pascau, A., Arici, M., and Llorente, V.J. (2017, October 4 – 8). Some progress on the use of the ENATE approach in 2D transport equations [Oral presentation]. 4th International Conference on Computational and Experimental Science and Engineering, Kemer, Turkey.
Llorente, V.J., and Pascau, A. (2017, September 13 – 15). ENATE scheme for coupled systems of transport equations [Oral presentation]. ECCOMAS Young Investigator Conference, Milan, Italy.
Llorente, V.J., and Pascau, A. (2017, July 3 – 5). ENATE scheme for two-dimensional problems [Oral presentation]. Congress on Numerical Methods in Engineering, Valence, Spain.
Llorente, V.J., and Pascau, A. (2017, July 3 – 5). Accuracy of ENATE scheme for the two-dimensional Poisson equation [Oral presentation]. Congress on Numerical Methods in Engineering, Valence, Spain.
2016
Pascau, A., Arici, M., and Llorente, V. (2016, July 11 – 15). ENATE procedure for the Navier-Stokes equations [Paper presentation]. 9th International Conference on Computational Fluid Dynamics, Istanbul, Turkey.
Pascau, A., Arici, M., and Llorente, V. (2016, June 5 – 10). Discontinuous Galerkin Spectral Element Method and ENATE approach comparison in 2D transport equations [Paper presentation]. VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete, Greece.
2015
Pascau, A., and Llorente, V.J. (2015, October 14 – 19). CFD calculations of MRF in valve mode [Oral presentation]. 2nd International Conference on Computational and Experimental Science and Engineering, Kemer, Turkey.
Invited Talks and Organized Workshops
2022
Mini-symposium "Mathematical modelling and numerical analysis for computational fluid dynamics" (MS2), at the Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications, Jaca, Spain; September 7 – 9, 2022. Organizers: V. Llorente and A. Navas.
Projects
Participation as researcher in R&D and innovation projects
SIMOPAIR: Simulaciones de alta precisión y modelización para diseño óptimo aeronáutico
Grant number: RTI2018-097075-B-I00
Sponsor: Ministerio de Ciencia e Innovación & AEI
Participating institutions: UPM & AIRBUS
PI: Eusebio Valero
Duration: Aug. 26, 2019 – Aug. 26, 2023
Amount: 169.400,00 €
NextSim - CODA: Next Generation of Industrial Aerodynamic Simulation Code
Grant number: 956104
Sponsor: EuroHPC & AEI
Participating institutions: BSC, UPM, CIMNE, ONERA, DLR, CERFACS, & AIRBUS
PI: Oriol Lehmkuhl, Eusebio Valero, Jordi Pons-Prats, Stefan Görtz, Marc Montagnac, Vincent Couaillier
Duration: Mar. 01, 2021 – Feb. 29, 2024
Amount: 3.978.096,75 € (1.884.704,63 from UE)
Grupo Consolidado T21 Mecánica de Fluidos Computacional
Code: 282215/3
Sponsor: Diputación General de Aragón, Fondo Social Europeo, & Universidad de Zaragoza
Participating institutions: UZ
PI: María Pilar García-Navarro
Duration: Apr. 25, 2016 – Oct. 31, 2017
Amount: 12.777,00 €