Application of the conservation element and solution element method in numerical modeling of heat conduction with melting and/or freezing

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used for the first time to solve phase change problems. Several isothermal phase change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate and robust for the numerical modeling of phase change problems.

[1]  Jim Douglas,et al.  On the numerical integration of a parabolic differential equation subject to a moving boundary condition , 1955 .

[2]  Virgil J. Lunardini,et al.  Heat transfer in cold climates , 1981 .

[3]  A. D. Solomon,et al.  Mathematical Modeling Of Melting And Freezing Processes , 1992 .

[4]  K. A. Rathjen,et al.  Heat Conduction With Melting or Freezing in a Corner , 1971 .

[5]  T. Z. Blazynski,et al.  Techniques of Analysis , 1976 .

[6]  C. M. Elliott,et al.  Weak and variational methods for moving boundary problems , 1982 .

[7]  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 .

[8]  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 .

[9]  Nan-Suey Liu,et al.  A Module for the NCC Solver Using the Concept of Space-Time Conservation Element and Solution Element , 2000 .

[10]  B. Boley.  A general starting solution for melting and solidifying slabs , 1968 .

[11]  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. 2; Numerical Simulation of Shock Waves and Contact Discontinuities , 1998 .

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

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

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

[15]  Philip C. E. Jorgenson,et al.  Prediction of Sound Waves Propagating Through a Nozzle Without/With a Shock Wave Using the Space-Time CE/SE Method , 2000 .

[16]  Nan-Suey Liu,et al.  AN ALTERNATIVE FLOW SOLVER FOR THE NCC - THE FLUX CODE AND ITS ALGORITHM , 2001 .

[17]  J. Crank.  Free and moving boundary problems , 1984 .

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

[20]  Kumar K. Tamma,et al.  On adaptive time stepping approaches for thermal solidification processes , 1992 .

[21]  Ching Y. Loh,et al.  Numerical Investigation of Transonic Resonance with a Convergent-Divergent Nozzle , 2002 .

[22]  Jennifer J. Zhao,et al.  Convergence and error bound analysis for the space-time CESE method , 2001 .

[23]  A. M. Meirmanov,et al.  The Stefan Problem , 1992 .

[24]  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 .

[25]  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 .

[26]  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 .

[27]  M. Cross,et al.  Accurate solutions of moving boundary problems using the enthalpy method , 1981 .