Browsing by Author "Smith, Matthew R."

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Accurate True Direction Solutions to the Euler Equations Using a Uniform Distribution Equilibrium Method
(2010-07-01)
Ferguson, Alex
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Smith, Matthew R.
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Wu, J. -S.
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機械工程學系
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Department of Mechanical Engineering
A novel approach for the use of multiple continuous uniform distributions for reconstruction of the Maxwell-Boltzmann equilibrium probability distribution function is used for the solution of one and two dimensional Euler equations. The Uniform distribution Equilibrium Flux Method (UEFM) is a kinetic-theory based flux solver which calculates true directional, volume to volume fluxes based on integration (over velocity space and physical space) of a sum of uniform probability distribution functions working to approximate the equilibrium distribution function. The resulting flux expressions contain only the Heaviside unit step function and do not require the evaluation of the Exponential or Error Functions. The proposed method is verified using a series of one and two dimensional benchmarks and is shown to provide a higher level of accuracy (for a given computational expense) when compared to the similar Quiet Direct Simulation (QDS) method.
Development of a semi-implicit fluid modeling code using finite-volume method based on Cartesian grids
(2011-01-01)
Smith, Matthew R.
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Hung, Chieh-Tsan
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Lin, Kun-Mo
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Wu, Jong-Shinn
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Yu, Jen-Perng
Presented is the HLLG (Harten Lax and van Leer with Gradient inclusion) method for application to the numerical solution of general Partial Differential Equations (PDEs) in conservation form The HLLG method is based on the traditional HLL method with formal mathematical inclusion of gradients of conserved properties across the control volume employed for flux derivation The simple extension demonstrates that conventional higher extensions of the HLL method are mathematically inconsistent and produce various numerical instabilities The HLLG method with higher order extensions consistent with the flux derivation is absent of (or less affected by) the said numerical instabilities The HLLG method is then applied to solutions of the Euler Equations and the simulation of ID argon RF plasma simulation (C) 2010 Elsevier B V All rights reserved
Development of an improved spatial reconstruction technique for the HLL method and its applications
(2011-02-01)
Smith, Matthew R.
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Lin, K. -M.
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Hung, C. -T.
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Chen, Y. -S.
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Wu, J. -S.
The integral form of the conventional HLL fluxes are presented by taking integrals around the control volume centred on each cell interface. These integrals are demonstrated to reduce to the conventional HLL flux through simplification by assuming spatially constant conserved properties. The integral flux expressions are then modified by permitting the analytical inclusion of spatially linearly varying conserved quantities. The newly obtained fluxes (which are named HLLG fluxes for clarification, where G stands for gradient inclusion) demonstrate that conventional reconstructions at cell interfaces are invalid and can produce unstable results when applied to conventional HLL schemes. The HLLG method is then applied to the solution of the Euler Equations and Shallow Water Equations for various common benchmark problems and finally applied to a 1D fluid modeling for an argon RF discharge at low pressure. Results show that the correct inclusion of flow gradients is shown to demonstrate superior transient behavior when compared to the existing HLL solver and conventional spatial reconstruction without significantly increasing computational expense. (C) 2010 Elsevier Inc. All rights reserved.
GPU acceleration for general conservation equations and its application to several engineering problems
(2011-06-01)
Kuo, Fang-An
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Smith, Matthew R.
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Hsieh, Chih-Wei
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Chou, Chau-Yi
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Wu, Jong-Shinn
Presented is a general method for conservation equations called SHLL (split HLL) applied using Graphics Processing Unit (GPU) acceleration. The SHLL method is a purely vector-split approximation of the classical HLL method (Harten et al.. 1983 [1]) which assumes the presence of local wave propagation in the algebraic derivation of fluxes across cell surfaces. The conventional HLL flux expression terms are interface-split and wave propagation velocities estimated (where required) based on local conditions. Due to the highly local nature of the SHLL fluxes, the scheme is very efficiently applied to GPU computation since the flux, initialisation and update phases of the computation are all vectorized processes. The SHLL scheme is applied to GPU computating using Nvidia's CUDA package. Numerical schemes are presented for solutions to the general transport (convection-diffusion) equation, Euler Equations and Shallow Water Equations with results presented for several benchmark gas and shallow water flow engineering problems. Computational times are compared between high-end GPU (Nvidia C1060) and CPU (Intel Xeon 3.0 GHz, 32 MB cache) systems with reported speedups of over 67 times when applied to two dimensional simulations with multi-million cell numbers. (C) 2010 Elsevier Ltd. All rights reserved.
Hybrid OpenMP/AVX acceleration of a Split HLL Finite Volume Method for the Shallow Water and Euler Equations
(2015-03-30)
Liu, Ji-Yueh
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Smith, Matthew R.
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Kuo, Fang-An
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Wu, Jong-Shin
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機械工程學系
Presented is the application of the Split Harten, Lax and van Leer (SHLL) technique applied to parallel computation using a hybrid OpenMP/AVX parallelization paradigm for the Shallow Water Equations and Euler Equations. The key behind the ease of parallelization of the SHLL method for both governing equations is the mathematical/vector splitting in each coordinate direction - this splitting results in a high degree of locality, producing a scheme which is embarrassingly parallel and well suited for the vectorization capacities offered by vector-computing architectures. Here we demonstrate this capacity using the SIMD capacities of modern CPUs, namely the Advanced Vector eXtensions (AVX) capability of recent CPUs. The main feature of AVX is the capacity to perform SIMD operations on 8 floating point variables in parallel - an increase from 4 floating point variables as possible using the previous SIMD Streaming Extensions (SSE). Furthermore, since modern CPU\'s employ a large number of cores, we further extend the performance by using AVX on each available CPU core using shared memory (OpenMP) parallelization. We present a direction-split higher order extension to both the SHLL method and apply it to AVX through the use of intrinsic functions in the flux computation and state computation modules. High performance is obtained by ensuring that all flux computations are performed using only AVX intrinsic functions - no computations are performed in serial. Through this approach, a single workstation with 2x Xeon CPU\'s (16 physical cores) allows a performance increase of over 117 times that of a single core alone in the flux evaluation kernel. (C) 2014 Elsevier Ltd. All rights reserved.
Rapid optimization of blast wave mitigation strategies using Quiet Direct Simulation and Genetic Algorithm
(2010-06-01)
Smith, Matthew R.
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Kuo, Fang-An
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Hsieh, Chih-Wei
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Yu, Jen-Perng
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Wu, Jong-Shinn
Presented is a rapid calculation tool for the optimization of blast wave related mitigation strategies The motion of gas resulting from a blast wave (specified by the user) is solved by the Quiet Direct Simulation (QDS) method - a rapid kinetic theory-based finite volume method The optimization routine employed is a newly developed Genetic Algorithm (GA) which is demonstrated to be similar to a Differential Evolution (DE) scheme with several modifications lit any Genetic Algorithm, individuals contain genetic information which is passed on to newly created individuals in successive generations The results from unsteady QDS simulations are used to determine the individual's "genetic fitness" which is employed by the proposed Genetic Algorithm during the reproduction process The combined QDS/GA algorithm is applied to various test cases and finally the optimization of a non-trivial blast wave mitigation strategy Both QDS and the proposed GA are demonstrated to perform with minimal computational expense while accurately solving the optimization problems presented (C) 2010 Elsevier BV All rights reserved