Ingegneria Meccanica | FLUIDODINAMICA NUMERICA

cod. 0622300002

FLUIDODINAMICA NUMERICA

	0622300002
	DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
	EQF7
	MECHANICAL ENGINEERING
	2018/2019

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2018
	PRIMO SEMESTRE

TEACHING UNITS

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

PROFESSORS

	FLAVIO GIANNETTI T Curriculum
	PAOLO LUCHINI Curriculum

	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: KNOWLEDGE AND UNDERSTANDING OF THE NUMERICAL METHODS MOST USED IN ENGINEERING AND THE TYPICAL MULTI-DIMENSIONAL PROBLEMS OF FLUID DYNAMICS. • APPLYING KNOWLEDGE AND UNDERSTANDING: THE ABILITY TO ANALYZE AND NUMERICALLY SOLVE PRACTICAL PROBLEMS TYPICAL IN FLUID DYNAMICS • 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: KNOWLEDGE AND UNDERSTANDING OF THE NUMERICAL METHODS MOST USED IN ENGINEERING AND THE TYPICAL MULTI-DIMENSIONAL PROBLEMS OF FLUID DYNAMICS.

• APPLYING KNOWLEDGE AND UNDERSTANDING: THE ABILITY TO ANALYZE AND NUMERICALLY SOLVE PRACTICAL PROBLEMS TYPICAL IN FLUID DYNAMICS

• 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
	(EXERCISES 40%) • FINITE DIFFERENCES (6H): CLASSIFICATION OF NUMERICAL METHODS. DERIVATION OF FINITE-DIFFERENCE FORMULAS AND THEIR ACCURACY • HIGH-LEVEL LANGUAGES (4H): STRUCTURE AND STYLE OF A COMPUTER PROGRAM. • NUMERICAL SIMULATION OF LUMPED SYSTEMS (14H): 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 (16H): 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 (14H): 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 (12H): DERIVATION VIA ASYMPTOTIC EXPANSION. VON MISES TRANSFORM. SIMILARITY SOLUTIONS. NUMERICAL SOLUTION IN PRIMITIVE VARIABLES AND IN STREAM FUNCTION FORMULATION. • STOKES EQUATIONS (12H): 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 12H: DISCRETISATION OF CONVECTIVE TERMS: STREAM FUNCTION-VORTICITY AND PRIMITIVE VARIABLE FORMULATIONS. CONSERVATIVE DISCRETISATION AND IMPLICATIONS FOR NUMERICAL STABILITY.

Contents

(EXERCISES 40%)

• FINITE DIFFERENCES (6H): CLASSIFICATION OF NUMERICAL METHODS. DERIVATION OF FINITE-DIFFERENCE FORMULAS AND THEIR ACCURACY

• HIGH-LEVEL LANGUAGES (4H): STRUCTURE AND STYLE OF A COMPUTER PROGRAM.

• NUMERICAL SIMULATION OF LUMPED SYSTEMS (14H): 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 (16H): 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 (14H): 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 (12H): DERIVATION VIA ASYMPTOTIC EXPANSION. VON MISES TRANSFORM. SIMILARITY SOLUTIONS. NUMERICAL SOLUTION IN PRIMITIVE VARIABLES AND IN STREAM FUNCTION FORMULATION.

• STOKES EQUATIONS (12H): 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 12H: 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 AND AN ORAL EXAM. THE FIRST CONSISTS IN THE IMPLEMENTATION OF A COMPUTER CODE FOR THE NUMERICAL SOLUTION OF A TYPICAL FLUID DYNAMICS PROBLEM. THE LATTER AIMS TO ASCERTAIN THE LEVEL OF KNOWLEDGE ACHIEVED BY THE STUDENT ON BOTH THEORETICAL AND METHODOLOGICAL CONTENTS, AS WELL AS HIS COMMUNICATION SKILLS AND THE APPROPRIATE USE OF SCIENTIFIC TERMINOLOGY. THE FINAL GRADE WILL BE OUT OF THIRTY AND WILL CONSIDER THE MARKS OBTAINED IN BOTH THE ORAL AND WRITTEN TEST.

Verification of learning

THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS CERTIFIED BY PASSING A WRITTEN AND AN ORAL EXAM. THE FIRST CONSISTS IN THE IMPLEMENTATION OF A COMPUTER CODE FOR THE NUMERICAL SOLUTION OF A TYPICAL FLUID DYNAMICS PROBLEM. THE LATTER AIMS TO ASCERTAIN THE LEVEL OF KNOWLEDGE ACHIEVED BY THE STUDENT ON BOTH THEORETICAL AND METHODOLOGICAL CONTENTS, AS WELL AS HIS COMMUNICATION SKILLS AND THE APPROPRIATE USE OF SCIENTIFIC TERMINOLOGY. THE FINAL GRADE WILL BE OUT OF THIRTY AND WILL CONSIDER THE MARKS OBTAINED IN BOTH THE ORAL AND WRITTEN TEST.

	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)