Flavio GIANNETTI | NUMERICAL FLUID DYNAMICS

cod. 0622300002

NUMERICAL FLUID DYNAMICS

	0622300002
	DEPARTMENT OF INDUSTRIAL ENGINEERING
	EQF7
	MECHANICAL ENGINEERING
	2024/2025

CURRICULUM INTERDISCIPLINARY

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2018
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	ING-IND/06	9	90	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

EXAMS

	Exam	Date	Session
	FLUIDODINAMICA NUMERICA	06/05/2025 - 09:00	SESSIONE ORDINARIA

	Objectives
	THE COURSE HAS THE OBJECTIVE TO PROVIDE THE STUDENT WITH THE KNOWLEDGE OF THE MAIN NUMERICAL METHODS USED IN ENGINEERING, TAKING A CUE FROM THE TYPICAL MULTIDIMENSIONAL PROBLEMS OF THE FLUID DYNAMICS IN WHICH SUCH TECHNIQUES ARE USED. AT THE END OF THE COURSE STUDENTS WILL HAVE ACQUIRED THE FOLLOWING SKILLS AND ABILITIES: •KNOWLEDGE AND UNDERSTANDING: UNDERSTANDING AND PROFICIENCY IN NUMERICAL METHODS COMMONLY USED IN ENGINEERING AND TYPICAL MULTIDIMENSIONAL PROBLEMS OF FLUID DYNAMICS. SPECIFICALLY, THE COURSE AIMS TO PROVIDE STUDENTS WITH KNOWLEDGE OF: -FINITE DIFFERENCES AND FINITE ELEMENTS. CONCEPTS OF CONVERGENCE AND CONSISTENCY. -METHODS FOR SOLVING ONE-DIMENSIONAL INITIAL AND BOUNDARY VALUE PROBLEMS. -METHODS FOR SOLVING MULTIDIMENSIONAL ELLIPTIC, PARABOLIC, AND HYPERBOLIC PROBLEMS. -METHODS FOR SOLVING BOUNDARY LAYER EQUATIONS, STOKES EQUATIONS, AND NAVIER-STOKES EQUATIONS. • APPLIED KNOWLEDGE AND UNDERSTANDING: ABILITY TO ANALYZE AND NUMERICALLY SOLVE TYPICAL PRACTICAL PROBLEMS IN FLUID DYNAMICS: BY THE END OF THE COURSE, THE STUDENT SHOULD BE ABLE TO: -DISCRETIZE AND SOLVE TYPICAL ENGINEERING PROBLEMS NUMERICALLY. -DISCRETIZE AND SOLVE LINEAR AND NONLINEAR ELLIPTIC, PARABOLIC, AND HYPERBOLIC EQUATIONS. -DISCRETIZE AND SOLVE STEADY AND UNSTEADY BOUNDARY LAYER EQUATIONS, STOKES EQUATIONS, AND NAVIER-STOKES EQUATIONS IN SIMPLE GEOMETRIES. • MAKING JUDGMENTS: BEING ABLE TO IDENTIFY THE MOST APPROPRIATE METHODS FOR SOLVING ANALYTICAL AND NUMERICAL PROBLEMS RELATED TO THE CONTEXT UNDER CONSIDERATION • COMMUNICATION SKILLS: ABILITY TO WORK IN GROUPS AND EXPOSE TOPICS RELATED TO THE MATTER IN QUESTION • LEARNING SKILLS: THE ABILITY TO APPLY THEIR KNOWLEDGE TO CONTEXTS DIFFERENT FROM THOSE PRESENTED DURING THE COURSE AND ANALYSE IN DEPTH THE SUBJECT USING MATERIALS OTHER THAN THOSE PROPOSED

THE COURSE HAS THE OBJECTIVE TO PROVIDE THE STUDENT WITH THE KNOWLEDGE OF THE MAIN NUMERICAL METHODS USED IN ENGINEERING, TAKING A CUE FROM THE TYPICAL MULTIDIMENSIONAL PROBLEMS OF THE FLUID DYNAMICS IN WHICH SUCH TECHNIQUES ARE USED. AT THE END OF THE COURSE STUDENTS WILL HAVE ACQUIRED THE FOLLOWING SKILLS AND ABILITIES:

•KNOWLEDGE AND UNDERSTANDING: UNDERSTANDING AND PROFICIENCY IN NUMERICAL METHODS COMMONLY USED IN ENGINEERING AND TYPICAL MULTIDIMENSIONAL PROBLEMS OF FLUID DYNAMICS. SPECIFICALLY, THE COURSE AIMS TO PROVIDE STUDENTS WITH KNOWLEDGE OF:
-FINITE DIFFERENCES AND FINITE ELEMENTS. CONCEPTS OF CONVERGENCE AND CONSISTENCY.
-METHODS FOR SOLVING ONE-DIMENSIONAL INITIAL AND BOUNDARY VALUE PROBLEMS.
-METHODS FOR SOLVING MULTIDIMENSIONAL ELLIPTIC, PARABOLIC, AND HYPERBOLIC PROBLEMS.
-METHODS FOR SOLVING BOUNDARY LAYER EQUATIONS, STOKES EQUATIONS, AND NAVIER-STOKES EQUATIONS.

• APPLIED KNOWLEDGE AND UNDERSTANDING: ABILITY TO ANALYZE AND NUMERICALLY SOLVE TYPICAL PRACTICAL PROBLEMS IN FLUID DYNAMICS: BY THE END OF THE COURSE, THE STUDENT SHOULD BE ABLE TO:
-DISCRETIZE AND SOLVE TYPICAL ENGINEERING PROBLEMS NUMERICALLY.
-DISCRETIZE AND SOLVE LINEAR AND NONLINEAR ELLIPTIC, PARABOLIC, AND HYPERBOLIC EQUATIONS.
-DISCRETIZE AND SOLVE STEADY AND UNSTEADY BOUNDARY LAYER EQUATIONS, STOKES EQUATIONS, AND NAVIER-STOKES EQUATIONS IN SIMPLE GEOMETRIES.

• MAKING JUDGMENTS: BEING ABLE TO IDENTIFY THE MOST APPROPRIATE METHODS FOR SOLVING ANALYTICAL AND NUMERICAL PROBLEMS RELATED TO THE CONTEXT UNDER CONSIDERATION

• COMMUNICATION SKILLS: ABILITY TO WORK IN GROUPS AND EXPOSE TOPICS RELATED TO THE MATTER IN QUESTION

• LEARNING SKILLS: THE ABILITY TO APPLY THEIR KNOWLEDGE TO CONTEXTS DIFFERENT FROM THOSE PRESENTED DURING THE COURSE AND ANALYSE IN DEPTH THE SUBJECT USING MATERIALS OTHER THAN THOSE PROPOSED

	Prerequisites
	FOR THE SUCCESSFUL ACHIEVEMENT OF THE OBJECTIVES IT IS REQUIRED THE KNOWLEDGE OF THE MOST COMMON NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS, QUADRATURE FORMULAS AND A BASIC KNOWLEDGE OF FLUID MECHANICS AS TAUGHT IN THE COURSE OFFERED DURING THE LAUREA TRIENNALE.

	Contents
	• FINITE DIFFERENCES (THEORY 4H, EXERCISES 2H): CLASSIFICATION OF NUMERICAL METHODS. DERIVATION OF FINITE-DIFFERENCE FORMULAS AND THEIR ACCURACY • HIGH-LEVEL LANGUAGES (THEORY 3H, EXERCISES 1H): STRUCTURE AND STYLE OF A COMPUTER PROGRAM. • NUMERICAL SIMULATION OF LUMPED SYSTEMS (THEORY 8H, EXERCISES 6H): INITIAL VALUES PROBLEMS AND THEIR SOLUTION VIA MULTI-STEP AND MULTI-STAGE METHODS. ZERO AND ABSOLUTE STABILITY. MODAL ANALYSIS. CONSISTENCY, STABILITY AND CONVERGENCE. BOUNDARY VALUE PROBLEMS AND THEIR SOLUTION VIA SHOOTING OR DIRECT METHODS. • NUMERICAL SOLUTION OF PROBLEMS DEPENDING ON SPACE AND TIME (THEORY 10H, EXERCISES 6H): CLASSIFICATION OF PDES. METHODS FOR 1D HEAT EQUATION AND THEIR STABILITY. SEMI-DISCRETISATION. HYPERBOLIC EQUATIONS AND THE THEORY OF CHARACTERISTICS. EQUATION OF CONVECTION AND ITS DISCRETISATION. CFL CONDITION. • NUMERICAL SOLUTION OF SPATIAL PROBLEMS IN 2D AND 3D (THEORY 8H, EXERCISES 6H): ELLIPTIC PROBLEMS AND THEIR SOLUTION BY DIRECT (LU DECOMPOSITION) AND ITERATIVE (JACOBI, GAUSS-SEIDEL, ADI) METHODS. ESTIMATE OF RESOLUTION TIME. OUTLINES OF MULTIGRID METHODS. • BOUNDARY LAYER EQUATIONS (THEORY 7H, EXERCISES 5H): DERIVATION VIA ASYMPTOTIC EXPANSION. VON MISES TRANSFORM. SIMILARITY SOLUTIONS. NUMERICAL SOLUTION IN PRIMITIVE VARIABLES AND IN STREAM FUNCTION FORMULATION. • STOKES EQUATIONS (THEORY 7H, EXERCISES 5H): CHARACTER OF THE EQUATIONS AND BOUNDARY CONDITIONS. PRIMITIVE VARIABLES AND STREAM FUNCTION - VORTICITY FORMULATION. COLOCATED AND STAGGERED GRIDS. SOLUTION VIA DIRECT AND ITERATIVE METHODS. PRESSURE CORRECTION METHOD. • NAVIER-STOKES EQUATIONS (THEORY 7H, EXERCISES 5H): DISCRETISATION OF CONVECTIVE TERMS: STREAM FUNCTION-VORTICITY AND PRIMITIVE VARIABLE FORMULATIONS. CONSERVATIVE DISCRETISATION AND IMPLICATIONS FOR NUMERICAL STABILITY.

Contents

• FINITE DIFFERENCES (THEORY 4H, EXERCISES 2H): CLASSIFICATION OF NUMERICAL METHODS. DERIVATION OF FINITE-DIFFERENCE FORMULAS AND THEIR ACCURACY

• HIGH-LEVEL LANGUAGES (THEORY 3H, EXERCISES 1H): STRUCTURE AND STYLE OF A COMPUTER PROGRAM.

• NUMERICAL SIMULATION OF LUMPED SYSTEMS (THEORY 8H, EXERCISES 6H): INITIAL VALUES PROBLEMS AND THEIR SOLUTION VIA MULTI-STEP AND MULTI-STAGE METHODS. ZERO AND ABSOLUTE STABILITY. MODAL ANALYSIS. CONSISTENCY, STABILITY AND CONVERGENCE. BOUNDARY VALUE PROBLEMS AND THEIR SOLUTION VIA SHOOTING OR DIRECT METHODS.

• NUMERICAL SOLUTION OF PROBLEMS DEPENDING ON SPACE AND TIME (THEORY 10H, EXERCISES 6H): CLASSIFICATION OF PDES. METHODS FOR 1D HEAT EQUATION AND THEIR STABILITY. SEMI-DISCRETISATION. HYPERBOLIC EQUATIONS AND THE THEORY OF CHARACTERISTICS. EQUATION OF CONVECTION AND ITS DISCRETISATION. CFL CONDITION.

• NUMERICAL SOLUTION OF SPATIAL PROBLEMS IN 2D AND 3D (THEORY 8H, EXERCISES 6H): ELLIPTIC PROBLEMS AND THEIR SOLUTION BY DIRECT (LU DECOMPOSITION) AND ITERATIVE (JACOBI, GAUSS-SEIDEL, ADI) METHODS. ESTIMATE OF RESOLUTION TIME. OUTLINES OF MULTIGRID METHODS.

• BOUNDARY LAYER EQUATIONS (THEORY 7H, EXERCISES 5H): DERIVATION VIA ASYMPTOTIC EXPANSION. VON MISES TRANSFORM. SIMILARITY SOLUTIONS. NUMERICAL SOLUTION IN PRIMITIVE VARIABLES AND IN STREAM FUNCTION FORMULATION.

• STOKES EQUATIONS (THEORY 7H, EXERCISES 5H): CHARACTER OF THE EQUATIONS AND BOUNDARY CONDITIONS. PRIMITIVE VARIABLES AND STREAM FUNCTION - VORTICITY FORMULATION. COLOCATED AND STAGGERED GRIDS. SOLUTION VIA DIRECT AND ITERATIVE METHODS. PRESSURE CORRECTION METHOD.

• NAVIER-STOKES EQUATIONS (THEORY 7H, EXERCISES 5H): DISCRETISATION OF CONVECTIVE TERMS: STREAM FUNCTION-VORTICITY AND PRIMITIVE VARIABLE FORMULATIONS. CONSERVATIVE DISCRETISATION AND IMPLICATIONS FOR NUMERICAL STABILITY.

	Teaching Methods
	THE COURSE CONSISTS OF A TOTAL OF 90 TEACHING HOURS (9CFU) DIVIDED AS FOLLOWS: 54 HOURS OF LECTURES AND 36 HOURS OF PRACTICE. DURING THE PRACTICING CLASSES THE NUMERICAL ALGORITHMS DISCUSSED DURING THE COURSE WILL BE IMPLEMENTED AND TESTED: CODES WILL BE DEVELOPED WITH THE ACTIVE PARTICIPATION OF STUDENTS.

	Verification of learning
	THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS CERTIFIED BY PASSING A WRITTEN TEST OF THE DURATION OF APPROXIMATELY TWO HOURS AIMED AT ASCERTAINING THE LEVEL OF KNOWLEDGE ACHIEVED BY THE STUDENT ON BOTH THEORETICAL AND METHODOLOGICAL CONTENTS OF THE COURSE, AS WELL AS PROGRAMMING AND COMMUNICATION SKILLS AND THE APPROPRIATE USE OF SCIENTIFIC TERMINOLOGY. THE FINAL GRADE WILL BE OUT OF THIRTY AND WILL CONSIDER THE MARKS OBTAINED IN THE DIFFERENT TESTS. THE MINIMUM GRADE (18 OUT OF 30) IS OBTAINED THROUGH A RIGHT MODELLING AND AN ENOUGH GOOD OVERALL KNOWLEDGE OF THE COURSE TOPICS. THE GRADE 30 OUT OF 30 IS PROPOSED TO THE STUDENTS WHO SHOW SOUND SOLUTION UNDER QUALITATIVE AND QUANTITATIVE POINT OF VIEWS WITH THOROUGH AND DEEP KNOWLEDGE OF THE COURSE TOPICS.

Verification of learning

THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS CERTIFIED BY PASSING A WRITTEN TEST OF THE DURATION OF APPROXIMATELY TWO HOURS
AIMED AT ASCERTAINING THE LEVEL OF KNOWLEDGE ACHIEVED BY THE STUDENT ON BOTH THEORETICAL AND METHODOLOGICAL CONTENTS OF THE COURSE, AS WELL AS PROGRAMMING AND COMMUNICATION SKILLS AND THE APPROPRIATE USE OF SCIENTIFIC TERMINOLOGY. THE FINAL GRADE WILL BE OUT OF THIRTY AND WILL CONSIDER THE MARKS OBTAINED IN THE DIFFERENT TESTS. THE MINIMUM GRADE (18 OUT OF 30) IS OBTAINED THROUGH A RIGHT MODELLING AND AN ENOUGH GOOD OVERALL KNOWLEDGE OF THE COURSE TOPICS.
THE GRADE 30 OUT OF 30 IS PROPOSED TO THE STUDENTS WHO SHOW SOUND SOLUTION UNDER QUALITATIVE AND QUANTITATIVE POINT OF VIEWS WITH THOROUGH AND DEEP KNOWLEDGE OF THE COURSE TOPICS.

	Texts
	TEXTBOOKS: 1) R. J. LEVEQUE: FINITE DIFFERENCE METHODS FOR ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS (SIAM 2007) 2) J. D. ANDERSON : COMMPUTATIONAL FLUID DYNAMICS . (MCGRAW HILL 1995) 3) P. LUCHINI: ONDE NEI FLUIDI, INSTABILITA E TURBOLENZA. DIPARTIMENTO DI PROGETTAZIONE AERONAUTICA, UNIVERSITA DI NAPOLI, 1993 ( AVAILABLE ON HTTP://ELEARNING.DIMEC.UNISA.IT) OTHER BOOKS: 1) P. LUCHINI, M. QUADRIO: AERODINAMICA. DIPARTIMENTO DI INGEGNERIA AEROSPAZIALE, POLITECNICO DI MILANO, 2000-2002; (AVAILABLE ON HTTPS://HOME.AERO.POLIMI.IT/QUADRIO/IT/DIDATTICA/DISPENSENUOVE.HTML E SU HTTP://ELEARNING.DIMEC.UNISA.IT) 2) S. K. GODUNOV, V. S. RIABENKI: DIFFERENCE SCHEMES (ELSEVIER 1987) 3) G. I. MARCIUK: METODI DEL CALCOLO NUMERICO (EDITORI RIUNITI 1984) 4) R. W. HAMMING: NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS (DOVER 1987) 5) R. J. LEVEQUE: NUMERICAL METHODS FOR CONSERVATION LAWS. (BIRKHAUSER 1992)

Texts

TEXTBOOKS:
1) R. J. LEVEQUE: FINITE DIFFERENCE METHODS FOR ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS (SIAM 2007)
2) J. D. ANDERSON : COMMPUTATIONAL FLUID DYNAMICS . (MCGRAW HILL 1995)
3) P. LUCHINI: ONDE NEI FLUIDI, INSTABILITA E TURBOLENZA. DIPARTIMENTO DI PROGETTAZIONE AERONAUTICA, UNIVERSITA DI NAPOLI, 1993 ( AVAILABLE ON HTTP://ELEARNING.DIMEC.UNISA.IT)
OTHER BOOKS:
1) P. LUCHINI, M. QUADRIO: AERODINAMICA. DIPARTIMENTO DI INGEGNERIA AEROSPAZIALE, POLITECNICO DI MILANO, 2000-2002; (AVAILABLE ON HTTPS://HOME.AERO.POLIMI.IT/QUADRIO/IT/DIDATTICA/DISPENSENUOVE.HTML E SU HTTP://ELEARNING.DIMEC.UNISA.IT)
2) S. K. GODUNOV, V. S. RIABENKI: DIFFERENCE SCHEMES (ELSEVIER 1987)
3) G. I. MARCIUK: METODI DEL CALCOLO NUMERICO (EDITORI RIUNITI 1984)
4) R. W. HAMMING: NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS (DOVER 1987)
5) R. J. LEVEQUE: NUMERICAL METHODS FOR CONSERVATION LAWS. (BIRKHAUSER 1992)

	More Information
	ITALIAN LANGUAGE TAUGHT SUBJECT. FURTHER INFORMATION ON THE COURSE (TEACHING MATERIAL, EXAMPLE SHEETS, CLASS TIMETABLE,.... ) IS AVAILABLE ON THE MOODLE SITE.

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Flavio GIANNETTI | NUMERICAL FLUID DYNAMICS