ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
The student knows and knows to apply the finite volume method in mathematical problems of environmental and industrial interest, in the context of nonlinear the hyperbolic laws of conservation in one and two dimensions. The proposed methods will be analyzed and validated with the tools of numerical analysis and, in some examples, with experimental datas in the propose practices.
1. Introduction: systems of hyperbolic conservation laws.
• Basic concepts and examples of environmental and industrial interest.
• Types of solutions: classic, weak and entropics
• The Riemann problem.
• Applications.
2. Finite Volume Methods for hyperbolic problems.
2.1 Resolution of linear onedimensional problems.
• Basic concepts
• Upwind methods
• Godunov method
• Stability conditions
• Applications.
2.2 Resolution of nonlinear onedimensional problems
• Conservative methods
• Upwind methods
• Lax-Wendroff theorem
• Godunov method
• Approximated Riemann solvers
• Flux vector splitting
• Conservative schemes for conservation laws with source terms
• Monotone schemes and TVD schemes
• Schemes consistent with the entropy condition
• Applications
2.3 Resolution of hyperbolic nonlinear bidimensional problems
• Dimensional-splitting schemes
• Finite volume definition on unstructured meshes
• Conservative shemes
• Conservative schemes for conservation laws with source terms
• Applications
Basic Bibliografy:
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E. Gowlewski e P.A. Raviart. Numerical Approximation for Hyperbolic Systems of Conservation laws, volume 118 of Applied Mathematic Sciences Springer, 1996.
R. LeVeque. Finite Volume Methods for Hyperbolic Poblems. Cambridge University Press. 2002.
E. F. Toro. Riemann solvers and Numerical Methods for fluids dynamics: a practical introduction. Springer-Verlag; Berlin, 3rd ed. 2009.
M. E. Vázquez-Cendón. Introducción al Método de Volúmenes Finitos. Colección de Manuais Universitarios. Servizo de Publicacións daUniversidad de Santiago de Compostela. 2008.
M. E. Vázquez-Cendón. Solving Hyperbolic Equations with Finite Volume Methods. Springer. 2015.
Complementary Bibliografy:
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B. van Leer. Towards the ultimate conservative difference schemes III. Upstream-centered difference schemes for ideal compressible flow. J. Comput. Phys., 23, 263-275. 1977.
S.K. Godunov. Ecuaciones de la Física Matemática. URSS. 1978
A. Harten, P. Lax e van Leer. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev., 25, 35-61. 1983
R. LeVeque. Numerical Methods for Conservation Laws. Basel. 1990.
E. F. Toro. Schock-capturing methods for free-surface shallow flows. John Wiley & Sons. 2001.
M. E. Vázquez-Cendón (Ed). Lecture notes on numerical methods for hyperbolic equations: short course book. 2011.
Basic:
CG3: To be able to integrate knowledge in order to state opinions using information that even incomplete or limited, include reflecting on social and ethical responsibilities linked to the application of their knowledge.
CG5: To have the appropriate learning skills to enable them to continue studying in a way that will be largely self-directed or autonomous, and also to be able to successfully undertake doctoral studies.
Specific:
CE4: To be able to select a set of numerical techniques, languages and tools, appropriate to solve a mathematical model.
Numerical simulation specialization:
CS2: To adapt, modify and implement software tools for numerical simulation.
To the students the basic notes of the matter will be facilitated to them containing proposed exercises, the indicated bibliography and in addition Web sites with complementary documentation and some basic publication to the subject.
The theoretical classes a presentation will be done of the contents proposing mathematical exercises on the methods and models to which they will be applied.
In the practical classes the exercises with the active participation of the students will be solved and the practices will be defined to implement in the computer. These classes will try to deepen in the understanding of the methods that will be applied to the numerical resolution of problems, affecting the validation of the results by means of analytical and/or experimental solutions, if it is possible.
CRITERIA FOR THE 1ST ASSESSMENT OPPORTUNITY
50% of the final grade: the students will present exercises and proyects to be evaluated. The skills developed in these tasks are: CG3, CG5, CE4 and CS2.
50% of the final grade: the students will sit an exam where they can use some helping materials. The skills developed in the exam are: CG3, CG5 and CE4.
CRITERIA FOR THE 2ND ASSESSMENT OPPORTUNITY
The same as in the first assessment opportunity.
- Use of the notes complementing with the bibliography of the topic and the problems of applications to solve.
- Work as a team to design and conduct or practices.
- Students may request tutoring through Skype, especially those living in other campus.
- It is recommended that you use the time of study in understanding the concepts and methods, see the bibliography and programming of the practices of the applications of paragraphs 2.1 , 2.2 and 2.3.
- As supplementary material students will have the taped lectures, which we call online-notes and the support of the virtual campus of the USC.
- Promote teamwork and group presentations and individual of the exercises in the lecture notes and in the practices, which will be delivered with a minimum amount of documentation that detail the aims of the practice or problems solved and the benefits of the method used with the appropriate validation.
PLAN DE CONTINGENCIA (para la adaptación de esta guía al documento Bases para el desarrollo de una docencia presencial segura en el curso 2021-2022 aprobado por él Consejo de Gobierno de lana USC en sesión común celebrada él día 30 de abril de 2021):
El procedimiento de evaluación es el mismo independientemente del escenario. En los escenarios en los que no sea factible realizar pruebas en alguna de las cinco sedes del M2i serán en remoto.
Las clases se impartirán con los sistemas que indique el M2i, actualmente LifeSize, al mismo tiempo podrá emplearse MS Teams para las presentaciones y las pruebas de los estudiantes. La tutorías también se pueden solicitar por Skype o MS Teams en todos los escenarios.
Maria Elena Vazquez Cendon
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813196
- elena.vazquez.cendon [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 16:30-18:00 | Grupo /CLE_01 | Galician | Computer room 5 |
| Wednesday | |||
| 16:30-18:00 | Grupo /CLE_01 | Galician | Computer room 5 |