S. Clain, M.T. Malheiro, G.J. Machado, and R. Costa,
The structural method for ordinary differential equations,
arXiv, 2508.02440, 2025.
DOI: https://doi.org/10.48550/arXiv.2508.02440
R. Costa, S. Clain, G.J. Machado, and J.M. Nóbrega,
Very high-order accurate finite volume scheme for the streamfunction-vorticity formulation of incompressible fluid flows with polygonal meshes on arbitrary curved boundaries,
arXiv, 2506.05081, 2025.
DOI: https://doi.org/10.48550/arXiv.2506.05081
B. Ramôa, R. Costa, F. Chinesta, and J.M. Nóbrega,
An open-source framework for modeling the evolution of fiber orientation,
OpenFOAM Journal 5, 17-37, 2025.
DOI: https://doi.org/10.51560/ofj.v5.131.
M. Santos, A. Araújo, S. Barbeiro, S. Clain, R. Costa, and G.J. Machado,
Very high-order accurate discontinuous Galerkin method for curved boundaries with polygonal meshes,
Journal of Scientific Computing 100, 66, 2024.
DOI: https://doi.org/10.1007/s10915-024-02613-2.
J. Castro, J.M. Nóbrega, and R. Costa,
Computational framework to model the selective laser sintering process,
Materials 17(8), 1845, 2024.
DOI: https://doi.org/10.3390/ma17081845.
R. Costa, S. Clain, G.J. Machado, J.M. Nóbrega, H. Beirão da Veiga, and F. Crispo,
Imposing general slip conditions on curved boundaries for 3D incompressible flows with a very high-order accurate finite volume scheme on polygonal meshes,
Computer Methods in Applied Mechanics and Engineering 415, 116274, 2023.
DOI: https://doi.org/10.1016/j.cma.2023.116274.
B. Ramôa, R. Costa, F. Chinesta, and J.M. Nóbrega,
A semi-automatic approach based on the method of manufactured solutions to assess the convergence order in OpenFOAM,
OpenFOAM Journal 2, 148-165, 2022.
DOI: https://doi.org/10.51560/ofj.v2.75.
R. Costa, S. Clain, G.J. Machado, and J.M. Nóbrega,
Very high-order accurate finite volume method for the steady-state incompressible Navier-Stokes equations with polygonal meshes on arbitrary curved boundaries,
Computer Methods in Applied Mechanics and Engineering 396, 115064, 2022.
DOI: https://doi.org/10.1016/j.cma.2022.115064.
R. Costa, J.M. Nóbrega, S. Clain, and G.J. Machado,
High-order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing,
International Journal for Numerical Methods in Engineering 123(4), 1146-1185, 2022.
DOI: https://doi.org/10.1002/nme.6892.
R. Costa, J.M. Nóbrega, S. Clain, and G.J. Machado,
Efficient very high-order accurate polyhedral mesh finite volume scheme for 3D conjugate heat transfer problems in curved domains,
Journal of Computational Physics, 445, 110604, 2021.
DOI: https://doi.org/10.1016/j.jcp.2021.110604.
R. Costa, J.M. Nóbrega, S. Clain, and G.J. Machado,
Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts,
Computer Methods in Applied Mechanics and Engineering 357, 112560, 2019.
DOI: https://doi.org/10.1016/j.cma.2019.07.029.
R. Costa, J.M. Nóbrega, S. Clain, G.J. Machado, and R. Loubère,
Very high-order accurate finite volume scheme for the convection-diffusion equation with general boundary conditions on arbitrary curved domains,
International Journal for Numerical Methods in Engineering 117(2), 188-220, 2019.
DOI: https://doi.org/10.1002/nme.5953.
R. Costa, S. Clain, R. Loubère, and G.J. Machado,
Very high-order accurate finite volume scheme on curved boundaries for the two-dimensional steady-state convection-diffusion equation with Dirichlet condition,
Applied Mathematical Modelling 54, 752-767, 2018.
DOI: https://doi.org/10.1016/j.apm.2017.10.016.
R. Costa, S. Clain, and G.J. Machado,
A sixth-order finite volume method for the steady-state incompressible Stokes equations on staggered unstructured meshes,
Journal of Computational Physics 349, 501-527, 2017.
DOI: https://doi.org/10.1016/j.jcp.2017.07.047.
R. Costa, S. Clain, G.J. Machado, and R. Loubère,
A very-high order accurate staggered finite volume scheme for the stationary incompressible Navier-Stokes and Euler equations on unstructured meshes,
Journal of Scientific Computing 71, 1375-1411, 2017.
DOI: https://doi.org/10.1007/s10915-016-0348-9.
S. Clain, C. Reis, R. Costa, J. Figueiredo, M.A. Baptista, and J. Miranda,
Second-order finite volume with hydrostatic reconstruction for tsunami simulation,
Journal of Advances in Modeling Earth Systems 8(4), 1691-1713, 2016.
DOI: https://doi.org/10.1002/2015MS000603.
R. Costa, S. Clain, and G.J. Machado,
Sixth-order finite volume method for the 1D biharmonic operator: application to the intramedullary nail simulation,
International Journal of Applied Mathematics and Computer Science 25(3), 529-537, 2015.
DOI: https://doi.org/10.1515/amcs-2015-0039.
R. Costa, S. Clain, and G.J. Machado,
New cell-vertex reconstruction for finite volume scheme: application to the convection-diffusion-reaction equation,
Computers & Mathematics with Applications 68, 1229-1249, 2014.
DOI: https://doi.org/10.1016/j.camwa.2014.08.015.
R. Costa, S. Clain, and G.J. Machado,
Finite volume scheme based on cell-vertex reconstructions for anisotropic diffusion problems with discontinuous coefficients,
In: B. Murgante et al. (eds.), Computational Science and Its Applications — ICCSA 2014,
Lecture Notes in Computer Science 8579, 87-102, Springer, 2014.
DOI: https://doi.org/10.1007/978-3-319-09144-0_7.
R. Costa, S. Teixeira, and I. Loureiro,
Numerical modeling of the physical parameters of the environment in industrial contexts,
In: P.M. Arezes et al. (Eds.), International Symposium on Occupational Safety and Hygiene — SHO 2016,
Occupational Safety and Hygiene IV, 281-285, CRC Press, 2016.
Available here.
G.M. Magalhães, R. Costa, and J.M. Nóbrega,
Enhancing coupled numerical simulations of viscoelastic flows through physical property analysis,
AIP Conference Proceedings, 3400, 050001, AIP Publishing, 2025.
DOI: https://doi.org/10.1063/5.0282477.
J. Castro, J.M. Nóbrega, and R. Costa,
Computational modelling of the selective laser sintering process,
AIP Conference Proceedings 2997(1), 050001, AIP Publishing, 2023.
DOI: https://doi.org/10.1063/5.0159825.
R. Costa, S. Teixeira, and I. Loureiro,
Numerical assessment of thermal environments for decision-making in industrial engineering and management,
Proceedings of the ENEGI 2016, Encontro Nacional de Engenharia e Gestão Industrial,
November 17-18, 2016, Covilhã, Portugal,
28-29, ENEGI UBI, 2016.
URL: https://www.ubi.pt/Ficheiros/Paginas/684/Proceedings.pdf.
R. Costa, S. Clain, and G.J. Machado,
6-th order finite volume approximations for the Stokes equations with a curved boundary,
Proceedings of the SYMCOMP 2015, 2nd International Conference on Numerical and Symbolic Computation: Developments and Applications,
March 26-27, 2015, Faro, Portugal,
365-382, APMTAC, 2015.
URL: http://repositorium.sdum.uminho.pt/handle/1822/35092.
R. Costa, S. Clain, and G.J. Machado,
Bending of a beam with finite volume schemes,
Proceedings of the SYMCOMP 2013, International Conference on Algebraic and Symbolic Computation,
September 9-10, 2013, Lisbon, Portugal,
207-218, APMTAC, 2014.
URL: http://repositorium.sdum.uminho.pt/handle/1822/27452.
R. Costa and J.M. Nóbrega,
exaFOAM industrial benchmark B4 - Viscoelastic complex profile extrusion,
DaRUS, V1 , 2024.
DOI: https://doi.org/10.18419/darus-3797.
R. Costa and J.M. Nóbrega,
exaFOAM microbenchmark MB7 - Viscoelastic lid-driven cavity,
DaRUS, V1 , 2024.
DOI: https://doi.org/10.18419/darus-3798.
R. Costa and J.M. Nóbrega,
exaFOAM microbenchmark MB19 - Viscoelastic profile extrusion,
DaRUS, V1 , 2024.
DOI: https://doi.org/10.18419/darus-3799.
R. Costa,
Advanced computational methods towards high-performance polymer processing simulations,
(Doctoral thesis), University of Minho, Guimarães, Portugal, 2020.
URL: https://repositorium.sdum.uminho.pt/handle/1822/77102.
R. Costa,
Numerical modeling and assessment of the thermal environment in an industrial premise of automotive components,
(Master’s dissertation), University of Minho, Guimarães, Portugal, 2015.
URL: http://repositorium.sdum.uminho.pt/handle/1822/39251.