Some recent development of the numerical simulation methods for CFd Liu ruxun Dept of Math. USTC, Hefei anhui 230026, China liunx@ustc.edu.cn
Some recent development of the numerical simulation methods for CFD Liu Ruxun Dept.of Math., UST C, Hefei Anhui 230026, China liurx@ustc.edu.cn
What is Computational Fluid Dynamics(CFD)? CFD IS the systematic application of computing systems and computational solution techniques to mathematical models formulated to describe and simulate fluid dynamic phenomena Simulation is used by engineers and physicists to forecast or reconstruct the behaviour of an engineering product or physical situation under assumed or measured boundary conditions(geometry, initial states, loads, etc.) The importance simulation techniques have great developed in recent decade years 1. Research of models is the foundation [29]Quecedo M. et al, Comparison of two mathematical models for solving the dam break problems using the FEM method, Comput. Methods Appl. Mech. Engrg., 194(2005 )3984-4005 Adopted a wrong model 2. Advances in solution algorithms 3. Mathematical analysis(classic and numerical analysis, discrete mathematics) 4.comPuterScience(algorithms,codingsoftware 5. Visualization techniques Lab for Computational Fluid Dynamics May28,2004
What is Computational Fluid Dynamics (CFD) ? CFD is the systematic application of computing systems and computational solution techniques to mathematical models formulated to describe and simulate fluid dynamic phenomena. Simulation is used by engineers and physicists to forecast or reconstruct the behaviour of an engineering product or physical situation under assumed or measured boundary conditions (geometry, initial states, loads, etc.). The importance simulation techniques have great developed in recent decade years: 1.Research of models is the foundation [29] Quecedo M. et al, C omparison of two mathematical m o d els for solving the dam break probl ems using the FEM method, C o m put. Methods Appl. Mech. Engrg.,194(2005)39 8 4-40 05 Adopted a wrong m o d el!! 2.Advances in solution algorithms 3.Mathematical analysis (classic and numerical analysis, discrete mathematics) 4.Computer Science (algorithms, coding, software) 5.Visualization Techniques Lab for Computational Fluid Dynamics May 28, 2004
Content 1. Introduction 2. Dome classical methods 2-1. Donor and Acceptor 2-2. Harlow and Welch's MAC Marker and cell), PIC, FLIC 3. Leonard's qUick (quadratic upstream interpolation for convective kinetics) and Simple 2-4. van Leer's MUSCL (monotonic upstream scheme for conservation law) 2-5. Collela's PPM(piecewise parabolic method) 2-6. Harten's TVD (total variation diminishing schemes) 3. Recent development of numerical simulation method 3-1. ENo (essentially non-oscillatory schemes) and weighted ENO 3-2. FVM(finite volume methods)with unstructured meshes 3-3. Rational approximation methods, high order compact and Pade schemes 3-4 CIP (cubic interpolated propagation methods) 3-5 VOF (volume of fluid) and Level set methods for tracking moving interface 3-6. DG Discontinuous Galerkin finite element methods) 3-7 LBM ( Lattice Boltzmann method 3-8. SPH (smoothed particle hydrodynamics )and meshless methods 3-9. Software: Fleunt phoenics Star-CD, CFX, and so on
Content 1.Introduction 2.Some classical methods 2-1.Donor and Acceptor 2-2.Harlow and Welch’s MAC (Marker and cell),PIC,FLIC 2-3.Leonard’s QUICK (quadratic upstream interpolation for convective kinetics) and Simple 2-4.van Leer’s MUSCL (monotonic upstream scheme for conservation law) 2-5.Collela’s PPM (piecewise parabolic method) 2-6.Harten’s TVD (total variation diminishing schemes) 3.Recent development of numerical simulation method 3-1.ENO (essentially non-oscillatory schemes) and weighted ENO 3-2.FVM (finite volume methods) with unstructured meshes 3-3.Rational approximation methods, high order compact and Pade schemes 3-4.CIP (cubic interpolated propagation methods) 3-5.VOF (volume of fluid) and Level Set methods for tracking moving- interface 3-6.DG (Discontinuous Galerkin finite element methods) 3-7.LBM (Lattice Boltzmann method ) 3-8.SPH (smoothed particle hydrodynamics)and meshless methods. 3-9.Software:Fleunt, Phoenics,Star-CD,CFX,and so on
1 Introduction In recent years the numerical methods of subtly simulate fluid dynamic phenomena have been advanced quickly and have succeeded in various fluid dynamICS applications In the short paper, only some important and effective new approaches will be introduced. Some methods, such as moving FEM, BEM, moving grid methods, spectral method LEs. multi-scale method and so on isn 't able to be discussed
1.Introduction In recent years, the numerical methods of subtly simulate fluid dynamic phenomena have been advanced quickly and have succeeded in various fluid dynamics applications. In the short paper, only some important and effective new approaches will be introduced. Some methods, such as moving FEM, BEM, moving grid methods, spectral method, LES, multi-scale method and so on, isn’t able to be discussed
2. Some classical methods we review some classical numerical methods in order to uss recent methods and developments easily 1. Donor and Acceptor methods Consider the numerical flux scheme(8) of the Id shallow water equations in the cell 1;=[x-1/2,x, +/2 ]and the neighboring cell I +=[x +/2,x +3/2].The numerical flux F(ua)at the discontinuous joint) point x=x,+/2 can be reconstructed by judging which is the donor-or acceptor-cell between the two cells (h) F(1+2) as u m>05or i+1 (h2+gh2), -(h2+8gh2)1 asl12<0(1) The reconstruction approach is called donor-acceptor method which has obvious mechanics character
2.Some classical methods we review some classical numerical methods in order to discuss recent methods and developments easily. 2-1.Donor and Acceptor methods Consider the numerical flux scheme (8) of the 1D shallow water equations in the cell and the neighboring cell .The numerical flux at the discontinuous (joint) point can be reconstructed by judging which is the donoror acceptor-cell between the two cells (1) The reconstruction approach is called donor-acceptor method which has obvious mechanics character. 1 1/ 2 2 2 1 1 1/ 2 2 2 1/ 2 2 2 1 ( ) , ( ) , ( ) 0 0 ( ) , ( ) , i i i i i i i hu hu F U a s u o r a s u hu gh hu gh + + + + + ⎧ ⎫ ⎧ ⎫ = ⎨ ⎬ > < ⎨ ⎬ + − + ⎩ ⎭ ⎩ ⎭ 1/ 2 1/ 2 [ , ] i i i I x x = − + 1 1/ 2 3/ 2 [ , ] i i i I x x + + = + 1/ 2 ( ) F Ui+ 1 1/ 2 x x = +