CFD Lecture 02 Phases of Modeling and Simulation(2015)

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Modeling & Simulation 
in CFD
Phases of Computational Modeling & 
Simulation
Physical System 
(Existing or Proposed)
Conceptual 
Modeling
Mathematical 
Modeling
Numerical 
Discretization
Computer 
Programming
Numerical Solution 
of the Computer 
Program
Representation of 
Numerical Solution 
Conceptual Modeling of the 
Physical System
To develop specification of the physical 
systems and its environment:
– Identifying the relevant physical events, 
or sequence of events;
– Determining the possible coupling of 
different physical processes.
Mathematical Modeling of the Physical System (a)
(a) Introducing simplifications/assumptions into the 
mathematical model of the physical system 
considered. 
Usually, the simplifications are made for either of 
the following aspects:
the dimensionality of the problem
or
the geometry 
or
the equations
or
possibly all three
Mathematical Modeling of the Physical System (b)
(b) Complete formulation of all of the partial 
differential equations (PDEs) for all elements of the 
physical system, i.e.
conservation equations
and 
auxiliary closure models
(c) Specification of all appropriate initial/boundary 
conditions for the physical system
Mathematical Modeling of the Physical System (c)
Observations:
– As a rule the simpler the geometry that one is 
willing to accept the more physics that can be 
included in the model.
– Restrictions of computer time and storage may 
limit the range of physical and geometrical 
scales that can be simulated.
– A model of limited, but known, applicability is 
often more useful than a more complete model.
– Any mathematical model, regardless of its 
physical level of detail, is by definition a 
simplification of reality.
Discretization of the Mathematical Model
Discretization of continuum domain into a finite 
numbers of discrete sub-domains (i.e. grid or mesh 
generation)
Conversion of continuum mathematics into discrete 
mathematics, i.e. discretization of differential 
equations
Development of numerical algorithms and solution 
procedures for solving the discrete equations
Discretization of Continuum Domain
Discretization of Differential Equations
In the equation discretization phase, the following 
questions are to be dealt with:
– Consistency of the discrete equations with the 
PDEs
– Stability of the numerical method
– Approximation of mathematical singularities
– Differences in zones of influence between the 
continuum and discrete systems
Numerical Algorithm Development
Algorithm development depends on 
extending concept of numerical analysis with 
close attention to the compatibility between:
– algorithm
and 
– computer architecture
Classification of Computers (a)
Microcomputer (PC)
Workstation
Minicomputer (Obsolete)
Mainframe/Server
Supercomputer (having the order of giga (109 ) 
flops)
Classification of Computers (b)
SISD (Sequential Instruction, Single-Data stream) 
Machine that processes data through a single CPU, 
executing one instruction after another
SIMD (Sequential Instruction, Multiple-Data stream) 
Machine that has several processing units, all 
supervised by a string control unit. Each processor 
receives the same instruction at any cycle but 
utilizes different data coming in separate data 
streams; e.g. A vector processor (also called an 
array processor)
MIMD (Multiple Instruction, Multiple-Data stream) 
Machine (the most promising of the assemblies for 
parallel processing) that uses many processing units, 
each executing instructions and utilizing data that 
are independent of the instructions and data used by 
the other CPUs
Evolution of CPU Performance
Computer Programming of the Discrete 
Model
Conversion of the numerical algorithms and 
solution procedures adopted into a computer 
program code.
Verification and Validation of the computer 
code.
Classification of Computer Code
Research code is to explore feasibility, 
understanding and potential for future 
applications
Production code is for direct application by 
an independent user. 
A production code must be:
– "ROBUST"
– "USER FRIENDLY" in the sense that the code is 
clearly expressed, well documented and 
straightforward to use; above all its limitations and 
accuracy must be clearly identified.
What is Verification of Computational 
Solution?
Verification is the process to determine 
whether the mathematical model is solved 
correctly, i.e.
Solving the Equations Right
Verification of Computer Code
A computer code should be verified by 
its author concerning:
1. the internal numerical accuracy of a code
2. the sensitivity of results to variations in 
the numerical algorithms adopted
3. the accuracy and implementation of 
boundary/initial conditions
What is Validation of Computational 
Solution?
Validation is the process of assessing 
the accuracy of the simulation model 
for its domain of application, i.e.
Solving the Right Equations:
Right model equations
Right numerical techniques
Validation Process of Computer Code
a) Numerical validation of the numerical scheme 
which includes grid-size and time-step refinement 
study to verify:
• the consistency of the scheme
• the convergence of the numerical solution
b) Validation of the computer code against 
benchmark solutions for specific classes of 
problems.
c) Comparison with the reliable experimental results 
to assess: 
• the physical approximations 
• the underlying assumptions
• the overall quality of the solution
Experimental Works to Support CFD
• To provide data for the evaluation of a 
mathematical model, it requires that all the 
initial/boundary conditions are the same in both 
computation and experiment
• To supplement a mathematical model by 
providing empirical data, e.g. turbulence 
modeling constants
• To provide information about flow phenomena 
prior to mathematical modeling
Validation against Experiment
Numerical Solution of the Computer 
Program Model
Generating numerical solution on a specified spatial 
grid size and distribution using a specified time step:
Issues to be dealt with:
– Spatial convergence
– Temporal convergence
– Iterative convergence
– Round-off error of computer
Performing parametric simulations of the physical 
system
Representation of the Numerical 
Solution
To present and interpret properly the 
computational solution through:
– Determining the best methods of 
presenting the numerical solution to the 
intended audiences
– Construction of continuous functions 
based on the discrete solutions obtained
Numerical Flow Visualization
2D/3D contour plots of scalar quantities
Velocity vector presentation
Particle tracing (streak lines)
Animated flow visualization (movies)
Contour Plots
Velocity Vector Field
Streaklines Plot
(Flow over an inclined plate)
Streaklines Plot
(Wing vortex form F-20)
An Example of Modeling & Simulation
In a Fast Breed Reactor (FBR) vessel, coolant flow issued from 
core is deflected by upper core structure, rises along vessel wall, 
impinging on free surface as shown below. Water experiments of 
simplified geometry of such situation in FBR vessel were 
performed in order to investigate the interaction of free surface 
and flow impinging on free surface.
Tentative Topics
1. Partial Differential Equations
2. Numerical Discretization of PDEs
3. Solution of Linear Equation Systems
4. Numerical Solutions for Model Transport 
Equations
5. Numerical Solution of Incompressible 
Flows
END
Invest time sufficiently and effectively
CFD could be fun/enjoyable to learn
	Modeling & Simulation in CFDPhases of Computational Modeling & Simulation
	Conceptual Modeling of the Physical System
	Mathematical Modeling of the Physical System (a)
	Mathematical Modeling of the Physical System (b)
	Mathematical Modeling of the Physical System (c)
	Discretization of the Mathematical Model
	Discretization of Continuum Domain 
	Discretization of Differential Equations
	Numerical Algorithm Development
	Classification of Computers (a)
	Classification of Computers (b)
	Evolution of CPU Performance
	Computer Programming of the Discrete Model
	Classification of Computer Code
	What is Verification of Computational Solution?
	Verification of Computer Code
	What is Validation of Computational Solution?
	Validation Process of Computer Code
	Experimental Works to Support CFD
	Validation against Experiment
	Numerical Solution of the Computer Program Model
	Representation of the Numerical Solution
	Numerical Flow Visualization
	Contour Plots
	Velocity Vector Field
	Streaklines Plot�(Flow over an inclined plate)
	Streaklines Plot�(Wing vortex form F-20)
	An Example of Modeling & Simulation
	Tentative Topics
	END