Implementation of monotonic higher order upwind scheme in KIVA 4

KIVA is a FORTRAN code developed by Los Alamos national lab to simulate complete engine cycle. KIVA is a flow solver code which is used to perform calculation of properties in a fluid flow field. It involves using various numerical schemes and methods to solve the Navier-Stokes equation. This project involves improving the accuracy of one such scheme by upgrading it to a higher order scheme. The numerical scheme to be modified is used in the critical final stage calculation called as rezoning phase. The primitive objective of this project is to implement a higher order numerical scheme, to validate and verify that the new scheme is better than the existing scheme. The latest version of the KIVA family (KIVA 4) is used for implementing the higher order scheme to support handling the unstructured mesh. The code is validated using the traditional shock tube problem and the results are verified to be more accurate than the existing schemes in reference with the analytical result. The convection test is performed to compare the computational accuracy on convective transfer; it is found that the new scheme has less numerical diffusion compared to the existing schemes. A four valve pentroof engine, an example case of KIVA package is used as application to ensure the stability of the scheme in practical application. The results are compared for the temperature profile. In spite of all the positive results, the numerical scheme implemented has a downside of consuming more CPU time for the computational analysis. The detailed comparison is provided. However, in an overview, the implementation of the higher order scheme in the latest code KIVA 4 is verified to be successful and it gives better results than the existing scheme which satisfies the objective of this project.

Topographic and meteorological influences on spatial scaling of heavy convective rainfall in mountainous regions

Characterizing the spatial scaling and dynamics of convective precipitation in mountainous terrain and the development of downscaling methods to transfer precipitation fields from one scale to another is the overall motivation for this research. Substantial progress has been made on characterizing the space-time organization of Midwestern convective systems and tropical rainfall, which has led to the development of statistical/dynamical downscaling models. Space-time analysis and downscaling of orographic precipitation has received less attention due to the complexities of topographic influences. This study uses multiscale statistical analysis to investigate the spatial scaling of organized thunderstorms that produce heavy rainfall and flooding in mountainous regions. Focus is placed on the eastern and western slopes of the Appalachian region and the Front Range of the Rocky Mountains. Parameter estimates are analyzed over time and attention is given to linking changes in the multiscale parameters with meteorological forcings and orographic influences on the rainfall. Influences of geographic regions and predominant orographic controls on trends in multiscale properties of precipitation are investigated. Spatial resolutions from 1 km to 50 km are considered. This range of spatial scales is needed to bridge typical scale gaps between distributed hydrologic models and numerical weather prediction (NWP) forecasts and attempts to address the open research problem of scaling organized thunderstorms and convection in mountainous terrain down to 1-4 km scales.