Courant Number and Mach Number Insensitive Ce/Se Euler Solvers

It has been known that the space-time CE/SE method can be used to obtain 1D, 2D, and 3D steady and unsteady o w solution with Mach number ranging from 0:0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embeded in a o w with the maxmum Mach number = 0:01.

[1]  Sin-Chung Chang,et al.  Treatments of stiff source terms in conservation laws by the method of space-time conservation element/solution element , 1997 .

[2]  Philip C. E. Jorgenson,et al.  Vortex dynamics simulation in aeroacoustics by the space-time conservation element and solution element method , 1999 .

[4]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[5]  Philip C. E. Jorgenson,et al.  Near Field Screech Noise Computation for an Underexpanded Supersonic Jet by the CE/SE Method , 2001 .

[6]  Philip C. E. Jorgenson,et al.  Accuracy Study of the Space-Time CE/SE Method for Computational Aeroacoustics Problems Involving Shock Waves , 2000 .

[7]  Sin-Chung Chang,et al.  Gust Acoustic Response of a Single Airfoil Using the Space-Time CE/SE Method , 2002 .

[8]  Sin-Chung Chang,et al.  The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 1; The Two Dimensional Time Marching Schemes , 1998 .

[9]  Theo G. Keith,et al.  Application of the conservation element and solution element method in numerical modeling of heat conduction with melting and/or freezing , 2003 .

[10]  Nan-Suey Liu,et al.  FLUX - An alternative flow solver for the National Combustion Code , 1999 .

[11]  L. Hultgren,et al.  Noise Computation of a Shock-Containing Supersonic Axisymmetric Jet by the CE/SE Method , 2000 .

[12]  Moujin Zhang,et al.  Solving Magnetohydrodynamic Equations Without Special Treatment for Divergence-Free Magnetic Field , 2004 .

[13]  C. Loh,et al.  Numerical Investigation of Transonic Resonance with a Convergent-Divergent Nozzle , 2002 .

[15]  Theo G. Keith,et al.  Application of the Conservation Element and Solution Element Method in Numerical Modeling of Axisymmetric Heat Conduction with Melting and/or Freezing , 2004 .

[16]  Thomas Molls,et al.  Space-Time Conservation Method Applied to Saint Venant Equations , 1998 .

[17]  Sin-Chung Chang,et al.  A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady euler equations using quadrilateral and hexahedral meshes , 2002 .

[18]  Sin-Chung Chang,et al.  Calculations of Low-Mach-Number Viscous Flows without Preconditioning by the Space-Time CE/SE Method , 2001 .

[19]  Ming Chia Lai,et al.  Direct Calculations of Cavitating Flows by the Space-Time CE/SE Method , 2001 .

[20]  Chang-Kee Kim,et al.  Cavity Flows in a Scramjet Engine by the Space-Time Conservation and Solution Element Method , 2004 .

[21]  Sin-Chung Chang,et al.  THE METHOD OF SPACE-TIME CONSERVATION ELEMENT AND SOLUTION ELEMENT — A NEW PARADIGM FOR NUMERICAL SOLUTION OF CONSERVATION LAWS , 1998 .

[22]  Theo G. Keith,et al.  Application of the CE/SE Method to Wave Journal Bearings , 2003 .

[23]  B. Vanleer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[24]  Khairul Q. Zaman,et al.  Investigation of a ‘transonic resonance’ with convergent–divergent nozzles , 2002, Journal of Fluid Mechanics.

[25]  Joseph Yen,et al.  Computational Aeroacoustics Using a Simplified Courant Number Insensitive CE/SE Method , 2005 .

[26]  S. Motz,et al.  Comparison of numerical methods for the simulation of dispersed phase systems , 2002 .

[27]  Theo G. Keith,et al.  Computation of Pressurized Gas Bearings Using the CE/SE Method , 2003 .

[28]  Philip C. E. Jorgenson,et al.  Numerical Simulation of Aeroacoustic Field in a 2D Cascade Involving a Downstream Moving Grid Using the Space-Time CE/SE Method , 2001 .

[29]  Wai Ming To,et al.  Application of the space-time conservation element and solution element method to one-dimensional convection-diffusion problems , 2000 .

[30]  X. Wang,et al.  Multi-Dimensional Courant Number Insensitive Euler Solvers for Applications Involving Highly Nonuniform Meshes , 2003 .

[31]  Sin-Chung Chang,et al.  Applications of the Space-Time Conservation Element/Solution Element Method to Unsteady Chemically Reacting Flows , 1997 .

[32]  Sin-Chung Chang,et al.  A 3-D non-splitting structured/unstructured Euler solver based on the space-time conservation element and solution element method , 1999 .

[33]  Philip C. E. Jorgenson,et al.  Computation of Feedback Aeroacoustic System by the CE/SE Method , 2001 .

[34]  Sin-Chung Chang,et al.  Courant Number Insensitive Transient Viscous Flow Solver Based on CE/SE Framework , 2005 .

[35]  Vigor Yang,et al.  Local Mesh Refinement in the Space-Time CE/SE Method , 2001 .

[36]  Wai Ming To,et al.  A brief description of a new numerical framework for solving conservation laws — The method of space-time conservation element and solution element , 1991 .

[37]  Philip C. E. Jorgenson,et al.  Robust and simple non-reflecting boundary conditions for the space-time conservation element and solution element method , 1997 .

[38]  Philip C. E. Jorgenson,et al.  Parallel CE/SE Computations via Domain Decomposition , 2001 .

[39]  Sten Bay Jørgensen,et al.  A novel partial differential algebraic equation (PDAE) solver: iterative space-time conservation element/solution element (CE/SE) method , 2004, Comput. Chem. Eng..

[40]  Sin-Chung Chang,et al.  Numerical simulation of flows caused by shock-body interaction , 1996 .

[41]  Ming Chia Lai,et al.  Simulation of Spray Transfer Processes in Electrostatic Rotary Bell Sprayer , 2004 .

[42]  B. Venkatachari,et al.  Development of a Transient Viscous Flow Solver Based on Conservation Element-Solution Element Framework. , 2004 .

[44]  Sin-Chung Chang,et al.  Regular Article: The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws , 1999 .

[45]  Sten Bay Jørgensen,et al.  A fast and accurate numerical method for solving simulated moving bed (SMB) chromatographic separation problems , 2004 .

[46]  Sin-Chung Chang,et al.  Wave computation in compressible flow using space-time conservation element and solution element method , 2001 .

[47]  Philip C. E. Jorgenson,et al.  Treating stiff source terms in conservation laws by the space-time conservation element and solution element method , 1998 .

[48]  Ming Chia Lai,et al.  Direct calculations of cavitating flows in fuel delivery pipe by the space-time CE/SE method , 1999 .

[49]  Sin-Chung Chang.  The Method of Space-Time Conservation Element and Solution Element-A New Approach for Solving the Navier-Stokes and Euler Equations , 1995 .

[50]  G. Sod.  A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[51]  G. D. van Albada,et al.  A comparative study of computational methods in cosmic gas dynamics , 1982 .

[52]  Sin-Chung Chang,et al.  Explicit Von Neumann Stability Conditions for the C-Tau Scheme: A Basic Scheme in the Development of the Ce-Se Courant Number Insensitive Schemes , 2013 .