The purpose of this work is to implement four additional inviscid flux methods in the U2NCLE solver being developed at Mississippi State University. The goal is that some or all of these methods may provide benefits over the current options with respect to accuracy or robustness. These four methods include both the Harten, Lax, Van Leer, Einfeldt (HLLE) and Harten, Lax, Van Leer ? Contact (HLLC) methods as well as the Advection Upstream Splitting Method (AUSM) and its successor AUSM+. The HLL family, which includes both HLLE and HLLC are based on the Riemann problem, which is divided into a number of states. The AUSM family attempts to combine the effects of both flux vector and flux difference splittings to create better schemes. Several simple and complex cases were run with each new method and compared to the methods currently available as well as experimental and analytical results when available. The results of the simple tests showed that all the methods were similarly suited for delivering accurate results on simple cases. In more complex cases, however, the AUSM family proved to be less robust and failed to converge for the final case. The HLLE method showed excellent robustness qualities but seemed to over predict the viscous values in several cases. The HLLC method proved equally as accurate and robust as Roe's Method.

The solid state, hydrothermal and flux methods were used for the investigation of alkaline earth and transition metal borophosphate compounds. The products and the phase relations were investigated by XRD, IR, DTA, and EDX methods. The solid state reactions of several boron compounds with different phosphating agents have been studied in the temperature range of 400-1200 oC. Hydrothermal and flux techniques were performed at 150 oC and 1200 oC, respectively. On the other hand, an attempt has been made to prepare a novel borophosphate compound MIIMIV[BPO7] (where MIV= Zr4+, Si4+, and MII= Sr2+, Ca2+) by solid state reactions and to investigate intermediate and final products. (NH4)2HPO4 and NH4H2PO4 were used as a phosphating agent. For the synthesis of these new compounds, the following reaction was predicted using the stoichiometric amount of the reactants: 2MIVO2 + 2MIICO3 + B2O3 + 2(NH4)2HPO4 &amp / #8594 / 2MIIO.MIVO2.B2O3.P2O5 + 4NH3 + 3H2O + 2CO2 (According to IUPAC formulation for the compounds composed of oxides) In the case of MIV=Zr4+ and MII=Sr2+, the formation of ZrSr[BPO7] was observed together with ZrO2 and SrBPO5. The formation of a new phase was proved by indexing the XRD pattern of the product after separating ZrO2 and SrBPO5 lines. Its crystal system was found to be orthorhombic and the unit cell parameters are a=11.85&Aring / , b=12.99 &Aring / , c=17.32 &Aring / . IR analysis shows that there is [BPO7]6- bands in the spectrum. At higher temperatures, Sr7Zr(PO4)6 was obtained. In the case of MIV=Si4+, SrBPO5 was the main product together with unreacted SiO2. At 1100 oC, Si4+ entered SrBPO5 structure and the product was indexed in orthorhombic system with a=8.9243 &Aring / , b=13.1548 &Aring / , and c=5.4036 &Aring / . Several other M:B:P ratios were tried for solid state systems. For compositions with different cations (such as Al3+, Ca2+, Na+), reactions generally pass through metal phosphates and BPO4. The X-ray diffraction powder pattern and infrared spectrum of several intermediate products obtained at different temperatures were presented and the several phase relations were investigated. The DTA and EDX analyses of some products were also reported.