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The primary objectives of this research are the development of algorithms which are applicable to non-linear continuum mechanic problems, especially to Stefan's Problems and Fluid Flows in Porous Media (Richard's Equation). We have studied 2-D and 3-D related problems. The codes are written in Cray Fortran and vectorization are done on the Cray Y-MP. The results obtained by Compact ADI, Finite Difference SOR and ADI are compared. It is seen that Compact ADI is superior. Six scientific research Papers have been presented/published in various conferences and journals in the last two years. All of the papers are attached in the appendix as attachments. Two senior faculty members worked in this project. Bolindra N. Borah (P.I.), Professor, North Carolina A&T State University, Robert E. White (Co-P.I.), Professor, North Carolina State University are the principal researchers. Besides, four graduate students participated in this project. Two have already completed the M.S. in Applied Mathematics while the other two are completing in the Spring Semester 1994.

The primary objectives of this research are the development of algorithms which are applicable to non-linear continuum mechanic problems, especially to Stefan's Problems and Fluid Flows in Porous Media (Richard's Equation). We have studied 2-D and 3-D related problems. The codes are written in Cray Fortran and vectorization are done on the Cray Y-MP. The results obtained by Compact ADI, Finite Difference SOR and ADI are compared. It is seen that Compact ADI is superior. Six scientific research Papers have been presented/published in various conferences and journals in the last two years. All of the papers are attached in the appendix as attachments. Two senior faculty members worked in this project. Bolindra N. Borah (P.I.), Professor, North Carolina A&T State University, Robert E. White (Co-P.I.), Professor, North Carolina State University are the principal researchers. Besides, four graduate students participated in this project. Two have already completed the M.S. in Applied Mathematics while the other two are completing in the Spring Semester 1994.

Direct numerical simulation of complex gas dynamics problems (computational experiment) is performed with the help of Euler, Navier-Stokes and Boltzmann equations. The basic principles of the computational experiment are formulated and the results for various gas dynamics problems of a complex internal structure are presented. The problems examined include the transonic regime (super-critical flows including transition through sound velocity), flows with a jet injected into the main stream and diffraction problems. Body wake flows are studied at various Reynolds numbers. The structure of a shock wave provides an example of rarefied gas flows at various Mach numbers. A set of control tests is worked out for the estimation of calculation accuracy. (Author)

Direct numerical simulation of complex gas dynamics problems (computational experiment) is performed with the help of Euler, Navier-Stokes and Boltzmann equations. The basic principles of the computational experiment are formulated and the results for various gas dynamics problems of a complex internal structure are presented. The problems examined include the transonic regime (super-critical flows including transition through sound velocity), flows with a jet injected into the main stream and diffraction problems. Body wake flows are studied at various Reynolds numbers. The structure of a shock wave provides an example of rarefied gas flows at various Mach numbers. A set of control tests is worked out for the estimation of calculation accuracy. (Author)

In this work, the fiber kinking phenomenon, which is known as the failure mechanism that takes place when a fiber reinforced polymer is loaded under longitudinal compression, is studied. A computational micromechanics model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking based on the deformation gradient decomposition (DGD) and the LaRC04 failure criteria.