Search

This paper presents the parallelization of two widely used implicit numerical solvers for the solution of partial differential equations on structured meshes, namely, the ADI (Alternating-Direction Implicit) solver for tridiagonal linear systems and the SIP (Strongly Implicit Procedure) solver for the penta-diagonal systems. Both solvers were parallelized using CUDA (Computer Unified Device Architecture) Fortran on GPGPUs (General-Purpose Graphics Processing Units). The parallel ADI solver (P-ADI) is based on the Parallel Cyclic Reduction (PCR) algorithm, while the parallel SIP solver (P-SIP) uses the wave front method (WF) following a diagonal line calculation strategy. To map the solution schemes onto the hierarchical block-threads framework of the CUDA on the GPU, the P-ADI solver adopted two mapping methods, one block thread with iterations (OBM-it) and multi-block threads (MBMs), while the P-SIP solver also used two mappings, one conventional mapping using effective WF lines (WF-e) with matrix coefficients and solution variables defined on original computational mesh, and a newly proposed mapping using all WF mesh (WF-all), on which matrix coefficients and solution variables are defined. Both the P-ADI and the P-SIP have been integrated into a two-dimensional (2D) hydrodynamic model, the CCHE2D (Center of Computational Hydroscience and Engineering) model, developed by the National Center for Computational Hydroscience and Engineering at the University of Mississippi. This study for the first time compared these two parallel solvers and their efficiency using examples and applications in complex geometries, which can provide valuable guidance for future uses of these two parallel implicit solvers in computational fluids dynamics (CFD). Both parallel solvers demonstrated higher efficiency than their serial counterparts on the CPU (Central Processing Unit): 3.73~4.98 speedup ratio for flow simulations, and 2.166~3.648 speedup ratio for sediment transport simulations. In general, the P-ADI solver is faster than but not as stable as the P-SIP solver; and for the P-SIP solver, the newly developed mapping method WF-all significantly improved the conventional mapping method WF-e. [ABSTRACT FROM AUTHOR]

A broad spectrum of model-derived weather datasets are available in the US. Because each product integrates atmospheric conditions with different model processes, each produces different statistical biases. This study validated air temperature from NLDAS-2 and a novel statistically downscaled NLDAS-2 against observational weather station data for the state of Florida. We statistically downscaled NLDAS-2 to a 1-km grid product using MODIS land surface temperature. We investigated mean biases and Pearson correlation coefficients between daily observational data and the two model-derived datasets. We then calculated multiple Climate Extremes Indices to further scrutinize differences in capturing extreme temperatures. Finally, we quantified potential causes of systematic NLDAS-2 biases related to distance from the coast, urban heat island, land cover, and type of observational stations. Two model-derived datasets showed similar mean biases and correspondence with observational data, underestimating maximum temperature by 1°C and overestimating minimum temperature by 2°C. Extreme temperatures were well simulated in both datasets. However, we still found overestimated extreme minimum temperatures and underestimated extreme maximum temperatures. Systematic biases tended to be higher for coastal stations and grids having a high fraction of water. Our study suggests that including physical processes covering land surface and ocean interactions may improve the model accuracy. [ABSTRACT FROM AUTHOR]