FLUIDODYNAMICS FOR ASTROPHYSICS

Course objectives

GENERAL OBJECTIVES: The main aim of the course is to introduce students to the basic equations describing fluid flows by mean of a careful mathematical treatment of the involved physical aspects. The Lagrangian and Eulerian views will be introduced and their applications to both ideal and realistic fluids and gases presented and discussed. In particular, the unavoidable numerical treatment of dynamics of gases and fluids in astrophysical conditions will be discussed. The, Lagrangian, Smooth Particle Hydrodynamics method (SPH) will be presented as one of the best suited to applications where a body force, like gravity, is present. At the end of the course the students should be able to deal with methods and basic techniques to deal with problems of dynamics of fluids in both terrestrial and astrophysical context. SPECIFIC OBJECTIVES: A - Knowledge and understanding OF 1) To know the constitutive equations underlying fluid dynamics and energetics. OF 2) To understand the physical processes that control the evolution of fluids, from gases to liquids and plasmas. OF 3) To understand the differences of the fluid dynamics in a terrestrial context respect to the astrophysical one. B - Application skills OF 4) To be able to apply, both on a theoretical and numerical side, the acquired knowledge to the interpretation and explanation of phenomena involving fluids in terrestrial and astrophysical context. C - Autonomy of judgment OF 5) To be able to evaluate the coherence between the physical framework and the mathematical scheme of representation adopted. D - Communication skills To be able to describe in a clear and critical way the contents of the various topics approached in the course. E - Ability to learn OF 6) Have the ability to deal with available didactic and scientific reference textbooks and papers in order to further explore some of the topics introduced during the course.

Channel 1
LUCA GRAZIANI Lecturers' profile

Program - Frequency - Exams

Course program
Knowledge of the physics of ideal and real fluids, including the ability to write key equations and solve some cases of physical and astrophysical interest. It also explores concepts of stability/instability and perturbation propagation. The theory of gravitational collapse and explosions will also be a focus of the course. Program (preliminary) Basic Concepts of Fluid Theory Real, Ideal, and Plasma Fluids Viscosity Compressive/Expansive Stresses and Shear Stresses Rigid Transformations and Deformability - Strain Rates Continuity of the Field Newtonian and Non-Newtonian Fluids Introduction to the Classical Continuous Field Field Lines and the Meaning of Divergence and Curl Key Equations of Ideal Fluids Lagrangian and Eulerian Description Continuity Equation Equation of Motion Energy Equation Thermodynamic Equation of State of the Fluid Modified Equations for Ideal Fluids Model of Forces in a Continuous Field Navier-Stokes Equations Thermodynamics of Real Fluids Stability and Instability Self-Gravitating Fluids Terrestrial and Astrophysical Fluids Jeans Collapse Fluid-Dynamic Instabilities The Role of Viscosity Shock Theory Structure and Behavior of Variables: Boundary Conditions Longitudinal and Tangential Discontinuities Shock Propagation: Mach Numbers Strong/Weak Shocks Astrophysical Examples of Shock Fronts Explosions and Perturbation Propagation Blast Waves Supernova Explosions Self-similar Solutions Turbulence The Laboratory and in Plasmas In Astrophysics Stellar Convection (Optional / Overview) Supersonic and Subsonic Flows (Optional / Overview) Winds Accretion Radiative Transport Problem Transport Equation Physical Processes: Absorption, Emission, Scattering Generalization to the Classical Continuous Field and PDE Theory The Density Function Key Theorems Elliptic/Parabolic/Hyperbolic Problems Method of Characteristics
Prerequisites
Prerequisites: 1. Vector Calculus and Mathematical Analysis. 2. Linear Geometry and Mathematical Methods of Physics. 3. Classical and Analytical Mechanics 4. Classical Electrodynamics To fill any gaps in the knowledge, the instructor will provide additional resources upon request.
Books
Physics of Fluids, R. Capuzzo Dolcetta, Springer (course reference text)
Frequency
Attendance is not mandatory but is strongly recommended to encourage interaction with the teacher.
Exam mode
The final exam consists of an oral exam with the instructor on the syllabus covered and requires the ability to solve some cases covered in class or their variations. The derivation of key equations and the proof of theorems covered in class are also required. The exam may be supplemented with an individual in-depth study on a topic agreed upon with the instructor, presented to the class before the final exam on Wednesdays from 8:00 to 9:00. Attendance is not mandatory, and the specific topic of the in-depth study is not part of the course syllabus. Please note that the various homework assignments are not mandatory and are not subject to ongoing assessment.
Bibliography
An Introduction to Astrophysical Hydrodynamics (S. N. Shore), Academic Press (only some sections indicated in class) Fluid Mechanics - Vol. 6 Course of Theoretical Physics, L. D. Landau, E. M. Lifschitz, Pergamon Press (only some sections indicated in class) Principles of Astrophysical Fluid Dynamics, C. Clarke and B. Carswell, Cambridge University Press (only some sections indicated in class) Physics of the Interstellar and Intergalactic Medium, B. Draine, Princeton University Press (only some sections indicated in class) Turbulence, an Introduction for Scientists and Engineers, P.A. Davidson, Cambridge University Press (only some sections indicated in class) The Equations of Radiation Hydrodynamics, Pomraning, Dover Publications (only some sections indicated in class) Accretion Power in Astrophysics, Frank, King, Raine, Cambridge University Press (only some sections indicated in class)
Lesson mode
Students who successfully complete the course, delivered in traditional, in-person format, will develop a knowledge of the physics of ideal and real fluids, being able to write key equations and solve some cases of physical and astrophysical interest. They will also delve into concepts of stability/instability and the propagation of perturbations. The theory of gravitational collapse and explosions will also be a focus of the course. Students are also encouraged to engage actively with the instructor to develop their own preferences for specific topics and seek individual in-depth study for the final exam.
LUCA GRAZIANI Lecturers' profile

Program - Frequency - Exams

Course program
Knowledge of the physics of ideal and real fluids, including the ability to write key equations and solve some cases of physical and astrophysical interest. It also explores concepts of stability/instability and perturbation propagation. The theory of gravitational collapse and explosions will also be a focus of the course. Program (preliminary) Basic Concepts of Fluid Theory Real, Ideal, and Plasma Fluids Viscosity Compressive/Expansive Stresses and Shear Stresses Rigid Transformations and Deformability - Strain Rates Continuity of the Field Newtonian and Non-Newtonian Fluids Introduction to the Classical Continuous Field Field Lines and the Meaning of Divergence and Curl Key Equations of Ideal Fluids Lagrangian and Eulerian Description Continuity Equation Equation of Motion Energy Equation Thermodynamic Equation of State of the Fluid Modified Equations for Ideal Fluids Model of Forces in a Continuous Field Navier-Stokes Equations Thermodynamics of Real Fluids Stability and Instability Self-Gravitating Fluids Terrestrial and Astrophysical Fluids Jeans Collapse Fluid-Dynamic Instabilities The Role of Viscosity Shock Theory Structure and Behavior of Variables: Boundary Conditions Longitudinal and Tangential Discontinuities Shock Propagation: Mach Numbers Strong/Weak Shocks Astrophysical Examples of Shock Fronts Explosions and Perturbation Propagation Blast Waves Supernova Explosions Self-similar Solutions Turbulence The Laboratory and in Plasmas In Astrophysics Stellar Convection (Optional / Overview) Supersonic and Subsonic Flows (Optional / Overview) Winds Accretion Radiative Transport Problem Transport Equation Physical Processes: Absorption, Emission, Scattering Generalization to the Classical Continuous Field and PDE Theory The Density Function Key Theorems Elliptic/Parabolic/Hyperbolic Problems Method of Characteristics
Prerequisites
Prerequisites: 1. Vector Calculus and Mathematical Analysis. 2. Linear Geometry and Mathematical Methods of Physics. 3. Classical and Analytical Mechanics 4. Classical Electrodynamics To fill any gaps in the knowledge, the instructor will provide additional resources upon request.
Books
Physics of Fluids, R. Capuzzo Dolcetta, Springer (course reference text)
Frequency
Attendance is not mandatory but is strongly recommended to encourage interaction with the teacher.
Exam mode
The final exam consists of an oral exam with the instructor on the syllabus covered and requires the ability to solve some cases covered in class or their variations. The derivation of key equations and the proof of theorems covered in class are also required. The exam may be supplemented with an individual in-depth study on a topic agreed upon with the instructor, presented to the class before the final exam on Wednesdays from 8:00 to 9:00. Attendance is not mandatory, and the specific topic of the in-depth study is not part of the course syllabus. Please note that the various homework assignments are not mandatory and are not subject to ongoing assessment.
Bibliography
An Introduction to Astrophysical Hydrodynamics (S. N. Shore), Academic Press (only some sections indicated in class) Fluid Mechanics - Vol. 6 Course of Theoretical Physics, L. D. Landau, E. M. Lifschitz, Pergamon Press (only some sections indicated in class) Principles of Astrophysical Fluid Dynamics, C. Clarke and B. Carswell, Cambridge University Press (only some sections indicated in class) Physics of the Interstellar and Intergalactic Medium, B. Draine, Princeton University Press (only some sections indicated in class) Turbulence, an Introduction for Scientists and Engineers, P.A. Davidson, Cambridge University Press (only some sections indicated in class) The Equations of Radiation Hydrodynamics, Pomraning, Dover Publications (only some sections indicated in class) Accretion Power in Astrophysics, Frank, King, Raine, Cambridge University Press (only some sections indicated in class)
Lesson mode
Students who successfully complete the course, delivered in traditional, in-person format, will develop a knowledge of the physics of ideal and real fluids, being able to write key equations and solve some cases of physical and astrophysical interest. They will also delve into concepts of stability/instability and the propagation of perturbations. The theory of gravitational collapse and explosions will also be a focus of the course. Students are also encouraged to engage actively with the instructor to develop their own preferences for specific topics and seek individual in-depth study for the final exam.
  • Lesson code1039018
  • Academic year2025/2026
  • CoursePhysics
  • CurriculumFisica applicata
  • Year3rd year
  • Semester1st semester
  • SSDFIS/05
  • CFU6