compressible flow course 1

Numerical Methods for Compressible Fluid MechanicsNumerical Methods for Compressible Fluid MechanicsNumerical Methods for Compressible Fluid MechanicsNumerical Methods for Compressible Fluid Mechanics1. Introduction

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Elizabeth Mickaily-Huber, Dominique Charbonnier, Jan B. Vos

course@cfse.chcourse@cfse.chcourse@cfse.chcourse@cfse.ch

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CFS Engineering, PSECFS Engineering, PSECFS Engineering, PSECFS Engineering, PSE----A, CHA, CHA, CHA, CH----1015 Lausanne1015 Lausanne1015 Lausanne1015 Lausanne

The course lecturers

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Dr. Elizabeth Mickaily Huber Dr. Dominique Charbonnier Dr. Jan B. Vos

Contents todays’ lecture

• Some words on who we are

• An example of studies we make• An example of studies we make

• Outline of the course

• Preparation of next week’s lecture

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Please switch off your mobile phones

Practical details

Course notes (polycopies) are the ones prepared by Dr. Alain Drotz + copies of the powerpoint presentations on the website of LIN

Please interrupt me to ask questions if something is not clear. Questions to me can be asked in English, French, German and Dutch

Exercises: two of the course days are reserved for exercises in a computer room

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Exercises: two of the course days are reserved for exercises in a computer room

Exam: orally, on the last day we will explain how the exam will be done

I have the habit to speak rapidly, please let me know if I go to fast !I have the habit to speak rapidly, please let me know if I go to fast !

Who I am

Some words about myself

Studied Aerospace Engineering at Delft University in the Netherlands,specialization Theoretical Aerodynamics. Master degree in 1982 on thespecialization Theoretical Aerodynamics. Master degree in 1982 on thedevelopment of a 1D CFD (Computational Fluid Dynamics) code for MagnetoHydrodynamic Flow simulations

PhD in 1987 at the Delft University of Technology, topic Combustion in Solid FuelRamjets (development of a 2D CFD code with combustion)

Worked at EPFL from 1987 to 1999, mainly on the development of 3D CFDcodes for Aerospace Applications

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codes for Aerospace Applications

Founded CFS Engineering in 1999 and continued to work on the use anddevelopment of CFD codes

A large experience in developing and using CFD codes for a wide variety of A large experience in developing and using CFD codes for a wide variety of

applicationsapplications

• CFS Engineering (Computational Fluids & Structures) is a spin-off company created in 1999 and located at the Business park of EPFL (École Polytechnique Fédérale de Lausanne)

who we are: CFS Engineering

• The major shareholder of CFS Engineering is RUAG Aerospace

Mission of CFS Engineering

To offer services in the numerical simulation of To offer services in the numerical simulation of

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To offer services in the numerical simulation of To offer services in the numerical simulation of

Fluid Mechanics and Structural Mechanics problemsFluid Mechanics and Structural Mechanics problems

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CFS Engineering – what do we do

Grid generation for fluid mechanics problems

Computational Fluid Dynamic simulations using the NSMB CFD code

Post-processing and analysis of the results

Coupled fluid dynamics-structural mechanics simulations using NSMB

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Adaptation of the NSMB code for specific applications

Ansys ICEM CFD Tetra, Prism and Hexa for mesh generation

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CFS Engineering – available tools

Ansys ICEM CFD Tetra, Prism and Hexa for mesh generation

Baspl++ and Paraview for visualization

B2000 for structural mechanics simulations

NSMB in house CFD code

Cluster of 10 Linux dual core PC’s for computing

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Several Linux PC workstations (organized in a cluster too)

CFS Engineering: NSMB CFD code (1)CFS Engineering: NSMB CFD code (1)

The NSMB code was initially developed at EPFL in 1991. From 1994 to 2003 it was further developed in the so called NSMB project, composed of KTH

CFS Engineering: NSMB code

was further developed in the so called NSMB project, composed of KTH (Stockholm), SAAB Military Aircraft (Linkoping), CERFACS (Toulouse), Airbus France (Toulouse) and EPFL (Lausanne).

Today NSMB is further developed in a consortium composed of RUAG Aerospace (Emmen), IMFT (Toulouse), IMFS (Strassbourg), TU Munchen, Univ. of the Army (Munchen), ASTRIUM-ST (Les Mureaux), EPFL, ETHZ and CFS Engineering.

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NSMB offers all functionalities which can be expected from a modern CFD tool used in the Aerospace industry (turbulence modeling, numerical schemes, moving grids, flexibility for complex geometries).

CFS Engineering: NSMB code (2)CFS Engineering: NSMB code (2)

CFS Engineering maintains the NSMB code, and is responsible for the parallelization of NSMB. CFS Engineering is working with PhD Students at

parallelization of NSMB. CFS Engineering is working with PhD Students at EPFL and ETHZ to extend the code with new turbulence and physical models.

CFS Engineering is working with SMR SA in Bienne to extend NSMB for the simulation of coupled engineering problems (fluid-heat transfer, fluid-structure).

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NSMB has been used by Airbus-France in the design of aircraft (Airbus A330, A340, A380, A400M).

CFS Engineering: NSMB code (3)CFS Engineering: NSMB code (3)

A340, A380, A400M).

NSMB is used by ASTRIUM-ST for flows over missiles and re-entry vehicles (including CFD simulations over the Rafale Fighter Aircraft)

NSMB is used by IMFT in Toulouse to flows over oscillating airfoils and wings, etc.

NSMB is used by KTH in Stockholm for unsteady simulations over delta wings.

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NSMB is used by CFS Engineering and RUAG Aerospace to simulate the flow over the FA-18 fighter, the flow over UAVs, the flow in base bleed units, supersonic air intake flows, flows in nozzles, flows over re-entry vehicles, etc.

Some figures (1)

Question: a numerical simulation that took 24 hours, 365 days in 1980 took how much time in 2005 ??

CFD: Introduction

much time in 2005 ??

1 second (a factor 32 million).

EPFL bought in 1989 a Cray 2 computer for more than 10 Million CHF. Today’s PC’s cost less than 1’000 CHF and deliver more computing power (a factor 10’000 in price).

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CFS Engineering: first PC cluster (1999) costed 20’000 CHF (6 PCs, 3GB total memory), last PC cluster (2008) costed 10’000 CHF (10 dual core PCs, 40 GB total memory) and is about 100 times faster.

Some figures (2)

Over the last 20 years, large investments were made in developing CFD codes:

CFD: Introduction

Improvement of numerical methods including parallel computing

Improvement of physical modeling (turbulence, transition, ..)

The cost reduction of computing power, combined with more efficient numerical schemes has lead to an increase of use of CFD in industry, since it is cheaper and faster than experimental testing, and provides better understanding of the physics.

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physics.

An example of an application studied at CFS Engineering

CFD: Example of application

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Example of Application: FA-18 Fighter

Motivations to discuss this example:

• Is concerned with CFD for compressible flows

• Shows an example of the use of CFD in industry

• Contains elements to future simulation environments

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FA-18 studies

RUAG Aerospace and CFS Engineering performed CFD simulations from 2001 to 2007 on the FA-18 fighter.

to 2007 on the FA-18 fighter.

2001: Compare CFD with Wind tunnel experiments.

2002: Extract Aerodynamic loads from CFD and compare with the Boeing Loads data base

2003: Sensitivity analysis different aircraft configurations

2004: Develop tool for static wing deformation

2005: New grid, study influence LEX fence, unsteady CFD for loads

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2005: New grid, study influence LEX fence, unsteady CFD for loads

2006: Dynamic Fluid Structure Interaction, influence SIWA fins on loads

2007: Study of Vertical Tail Buffeting

Components FAComponents FA--18 Fighter 18 Fighter –– CFD model 2005CFD model 2005

forward fuselage

center fuselage

aft fuselage

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forward fuselage

LEXILEF

wing rootwing fold

Grid Generation FAGrid Generation FA--1818

Different aircraft configurations

various control surfaces deflections

with and without weapons or fuel tanks!

Grid generated by ICEM CFD Hexa

contains ~ 14.0 Million grid points

contains around 3000 blocks

Replay files for control surface deflections and components addition or removal

various control surfaces deflections!

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To permit loads calculation on each aircraft component,

faces of a block single CAD surface familyMesh topology

each aircraft component

single CAD surface familyCAD surface families =

Cut on wingCut on wing

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Comparison CFD and Experiments, Mach=0.5Comparison CFD and Experiments, Mach=0.5

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Flow FeaturesFlow Features

StreamlinesMach = 0.95

Mach number contourssymmetry plan,

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symmetry plan, Mach = 0.95

Shock wavecanopy and fuselage near vertical fin

Aerodynamic Load Studies for the FAAerodynamic Load Studies for the FA--18 fighter18 fighter

The US Navy executed in the 1980s a flight test program with an

instrumented FA-18 fighter yielding the so called F4 Flight Test Data Base. Boeing used this data base to define different load cases for the Swiss FA-18 fleet, this is the Boeing Loads data base.

These data bases are incomplete for the conditions and usage of the Swiss FA-18 fighter (Swiss usage of the FA-18 fighter is three times more severe).

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A Full Scale Fatigue Test (FSFT) facility was build at RUAG.

CFD is used to provide the aerodynamic loads for different configurations (flap deflections, with/without fuel tanks), and flight conditions to complement the available load data bases.

Full Scale Fatigue Test rig at RUAG AerospaceFull Scale Fatigue Test rig at RUAG Aerospace

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CFD CFD –– Boeing Boeing -- and Flight data base correlationand Flight data base correlation

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Conclusions Aerodynamic Loads StudiesConclusions Aerodynamic Loads Studies

CFD – Flight load data base correlation:Much better than CFD Boeing load data base

Much better than CFD Boeing load data base

Computed aerodynamic loads in good agreement with measured loads in particular for AoA < 10

At AoA > 10: buffet, wing deformation, flow separation, unsteady effects become important

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CFD data makes more sense than Boeing loads data base, in particular on aft fuselage and horizontal stabilizer

Wing deformation – Tool Chain (1/4)

CFD NSMB calculation

Transfer CSM grid deformation into CFD

surface mesh displacement using

Transfer CFD loads to

CSM loads using FSCON

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CSM calculation

Fluid solution

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CSM calculation

Red points are the CSM grid nodes

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CSM calculation

Structural deformation

Remeshing andCFD NSMB calculation

deformed

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CSM calculation

Adaptation of the mesh

undeformed

Wing deformation Wing deformation –– pressure on wing of FApressure on wing of FA--18 Fighter18 Fighter

undeformed wing

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deformed wing

Static Deformation Static Deformation –– Wing elastic axisWing elastic axis

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FAFA--18 Unsteady flow simulations18 Unsteady flow simulations

Objective: Assess the influence of unsteady aerodynamic effects on the

Unsteady simulations using NSMB

aerodynamic loads

Strategy: Result of steady calculation used as initial solution

Assume flow symmetric

Detached Eddy Simulation (DES) for the turbulence

Dual time stepping approach

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Amount of data generated in the order of 350 Gbyte per case

Assume flow symmetric

0.5 seconds real time simulated

Computing time in the order of 3 weeks (2005)

Pressure and skin friction saved each time step

Complete solution every 20 steps

FAFA--18 Unsteady flow simulations18 Unsteady flow simulations

Mean value

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Dynamic Fluid Structure Interaction (FSI)Dynamic Fluid Structure Interaction (FSI)

Ingredients for dynamic Fluid Structure Interaction:

- Unsteady CFD solver with ALE formulation

- FSI transfer tool

- CSM solver (modal integration)

- Volume mesh deformation tool

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AGARD 445.6 WingAGARD 445.6 Wing

The AGARD 445.6 wing was has a 45o quarter chord sweep, and a

constant NACA64A004 symmetric profile

Measurements were made in the NASA Langley Transonic wind tunnel in 1963 to determine stability characteristics

Most published results are available for the so-called weakened wing in air

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For FSI calculations, four modes are considered, 2 bending modes and 4 torsional modes

Mode 1

Mode 2

Mode 3 Mode 4

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Mode 3 Mode 4

CFD Parameters:

Mach = 0.95

Rho_inf = 0.061 kg/m3

P_inf = 3500/4600/7000 Pa

Flutter index = 0.27/0.31/0.37

For this case the flutter boundary has a flutter index of 0.32.

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For this case the flutter boundary has a flutter index of 0.32.

Tests were made using different grid densities, different outer time steps, different time integration scheme, different values of the structural damping, different values of inner loop convergence criterium.

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FAFA--18 C2S825 Load case18 C2S825 Load case

Unsteady calculation with and without dynamic FSI

2000 time steps made to simulate 0.5 seconds of real time

Calculation time: about 10 days on a cluster of 10 PCs

Generated more than 1.4 TeraByte of data

Post processing took 2 days

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Post processing took 2 days

Flight results

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Source: NASA

Final Remarks FAFinal Remarks FA--18 studies18 studies

An example of the use of CFD in industry has been discussed

In 2001 we used CFD to predict steady aerodynamic forces and loads

In 2007 we used CFD to study coupled CFD-CSM unsteady phenomena

Today people are planning the simulation of the so called digital aircraft (CFD + Structures + Flight Mechanics)

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The way industry is using CFD is changing rapidly !

CFD: Course Outline

Outline of the CourseOutline of the Course

The course contains 3 modulesThe course contains 3 modules

I Introduction to unsteady flows

II Construction of higher order schemes

III Monotonic schemes of higher order

Which corresponds to the modules of the course given by Dr. Alain Drotz in

previous years.

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We modified the course, less theory, more directed to the use of numerical

methods in practice.

CFD: Course Outline

Module I: Introduction to unsteady flowsModule I: Introduction to unsteady flows

1. Introduction to the course (today)

2. 3D Euler equations

3. 1D Euler equations

4. Unsteady 1 dimensional flows

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4. Unsteady 1 dimensional flows

5. Introduction to the Riemann problem

CFD: Course Outline

Module II Construction of higher order schemesModule II Construction of higher order schemes

6. Conservative discretization schemes

7. Exercises

8. Classical finite difference schemes

9. Riemann problem and Roe scheme

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9. Riemann problem and Roe scheme

CFD: Course Outline

Module III Construction of higher order schemesModule III Construction of higher order schemes

10. Roe and AUSM schemes

11. Higher order monotonic schemes

12. Boundary conditions and preparation exercise 2

13. Exercises 2

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14. Preparation of Exam and Assessing the quality of numerical

simulations

TheTheTheThe orderorderorderorder ofofofof thethethethe lectureslectureslectureslectures maymaymaymay changechangechangechange somewhatsomewhatsomewhatsomewhat !!!!

CFD: Course Outline

What is a compressible flow?What is a compressible flow?

A compressible flow is a flow for which the density can not be consideredA compressible flow is a flow for which the density can not be considered

constant.

In general this occurs for air flows with a free stream Mach number larger than

What is a hypersonic flow?What is a hypersonic flow?

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Flows with a free stream Mach number larger than 5. At very high free stream

Mach numbers chemistry effects become important.

CFD: Course Outline

Flow over an Airfoil Flow over an Airfoil –– Mach number contoursMach number contours

Free stream Mach 0.745

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CFD: Course Outline

Flow over an Airfoil Flow over an Airfoil -- CpCp

Free stream Mach 0.745

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Navier Stokes equations

The The NavierNavier Stokes equations in vector & differential formStokes equations in vector & differential form

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Closure relations for the Closure relations for the NavierNavier Stokes equationsStokes equations

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How to solve these equations?How to solve these equations?

1. The difficulty of solving the Navier Stokes equations are the inviscid or1. The difficulty of solving the Navier Stokes equations are the inviscid or

convective terms => ignore for the moment the viscous terms (they are in

general approximated using 2nd order differences)

2. The compressible Euler and Navier Stokes equations permit

discontinuities in the solution (shock waves, expansion waves). The

numerical formulation needs to resolve these discontinuities.

3. Often different strategies for incompressible or compressible flows due to

the nature of the equations

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the nature of the equations

The Euler equations The Euler equations –– conservative formatconservative format

Incompressible flows: ρ is constant, energy equation is constant, energy equation is often not neededUnknowns: p, u, v, w

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To summarize (1)To summarize (1)

1. Compressible Euler equations: hyperbolic in time, unknowns are ρ, ρu,1. Compressible Euler equations: hyperbolic in time, unknowns are ρ, ρu,

ρv, ρw, ρE, 5 partial differential equations + 2 closure relations. Methods

solving the compressible Euler (or Navier Stokes) equations are in

general called density based.

2. Incompressible Euler equations: mixed parabolic-hyperbolic character,

unknowns are p, u, v, w. The continuity equation is a constraint to find

the pressure, and one can derive a pressure equation from the

continuity and momentum equations. Methods for solving the

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continuity and momentum equations. Methods for solving the

incompressible Euler (or Navier Stokes equations) are often called

pressure based due to the solution of a Poisson type equation for the

pressure.

To summarize (2)To summarize (2)

In the last 10 years convergence of the methodsIn the last 10 years convergence of the methods

• Incompressible, pressure based methods are extended to compressible

flows by including density gradients in the formulation for the pressure

equation

• Compressible, density based methods are extended to the

incompressible flow regime using pre-conditioning techniques

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Solution methods

Terminology (1)Terminology (1)

Partial differential equationPartial differential equation

Time discretization

Explicit scheme

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Implicit scheme

Solution methods

Spatial discretization: central schemes vs upwind schemes. In the group of

upwind schemes one has also TVD schemes and ENO schemes.upwind schemes one has also TVD schemes and ENO schemes.

Order of the schemes (spatial and/or in time): is linked to the truncation error

of the numerical discretization. Examples: first order, second order, third

order, etc.

Weak solution: solution which permits discontinuities (shock waves,

expansion waves)

Numerical flux: discretization of the physical flux f(U)

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Numerical flux: discretization of the physical flux f(U)

Limiter: is used with upwind schemes, and is a function of gradients to

eliminate oscillations. May give an upwind scheme the TVD property

Monotonic scheme: is represented by a monotonic decreasing or increasing

function

Solution methods

Properties Total Variation Diminishing (TVD) schemes:

• Are monotonic

• Should in principle not generate oscillations near shock waves

• Are stable

• Up to higher order (depends partly on the limiters)

• Are first order near extrema

• Do not always satisfy the entropy condition and thus may lead to wrong

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• Do not always satisfy the entropy condition and thus may lead to wrong

solutions

• Are very suitable for flows with shock waves

• Do not always give good results for low Mach number and incompressible

Upstream oscillation, decrease in amplitude, wrong location

Examples

wrong location

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Uncontrolled oscillations

Dissipation :

smearing out of the solution due to the numerical viscosity introduced by the space discretization

Examples

viscosity introduced by the space discretization scheme

Dispersion :

Lagging of the solution due to a numerical propagation velocity different from the exact one

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propagation velocity different from the exact one

Over/under shoots near shock and expansion waves which are

typical for higher order schemes

Examples

Lax - Wendroff

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Warming & Beam

Examples

MacCormack scheme without artificial dissipation

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MacCormack scheme with artificial dissipation

TVD scheme of Harten

Terminology

From PDE to Numerical Solution (1)From PDE to Numerical Solution (1)

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Terminology

From PDE to Numerical Solution (2)From PDE to Numerical Solution (2)

Stability: ensures that the numerical scheme does not permit errors to grow

Consistency: expresses that the discretized equations tend to the differential equations from which they are derived when ∆t and ∆x tend to zero

Convergence: the numerical solution should approach the exact solution of the partial differential equation at any point and at any time when ∆t and

Stability: ensures that the numerical scheme does not permit errors to grow indefinitely (errors should not be amplified by the numerical scheme)

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partial differential equation at any point and at any time when ∆t and ∆x tend to zero (ie when the mesh is refined or the time step reduced)

The end for today

That’s it for todayThat’s it for today

Any questions ?

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compressible flow course 1

Documents

compressible flow eqn

numerical compressible flow - casts.ntu.edu.tw

8 compressible flow

compressible fluid flow - saad

chapter 16 compressible flow

introduction to compressible flow

oosthuizen compressible fluid flow

ix. compressible flow - higher...

theory of compressible flow

notes(compressible flow)

compressible multiphase flow - cambridge

compressible fluid flow, oosthuizen

chapter 17: compressible flow

compressible flow introduction

compressible flow and sr71

compressible flow, iscetropic flow,

compressible flow range f300

$$$$ simulation compressible flow openfoam.pdf

compressible fluid flow

ch.12: compressible flow