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Showing 1 to 20 of 22 for “"WENO"”.
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Large Eddy Simulation of Supersonic Twin-Jet Impingement Using a Fifth-Order WENO Scheme
… terms are discretized using a fifth-order WENO scheme, whereas the viscous terms are discretized using a fourth-order central-differencing scheme. A low-storage five-stage fourth-order Runge-Kutta scheme is used to advance the solution in time. Code verification is achieved by comparison …
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A WENO finite difference scheme for a new class of Hamilton-Jacobi equations in electroelastostatics
… in the literature, including the so-called WENO finite difference schemes. These schemes, however, were developed and tested for special classes of Hamilton-Jacobi equations, which do not include the general type of Hamilton-Jacobi equation of interest in this work. The objective of this …
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A high-order Legendre-WENO numerical scheme for the non-conservative kernel density equations modeling particle-laden flows
… scheme with a Legendre basis. A standard WENO scheme is used by default, and a nonlinear mapping is introduced when needed to enforce physically relevant bounds in the solution, especially in areas of particle depletion. The strong stability preserving RK3 scheme is used to obtain high …
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Three Problems Involving Compressible Flow with Large Bulk Viscosity and Non-Convex Equations of State
… using a weighted essentially non-oscillatory (WENO) numerical scheme. We show that shock-induced separation can be suppressed once the bulk viscosity is large enough. In the third problem, we solve a quartic Burgers equation to describe the steady, two-dimensional, inviscid supersonic flow …
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Large eddy simulation of primary liquid-sheet breakup
… combustion codes. Both high-order linear and WENO schemes have been created for general polyhedral meshes. The notorious complexity of high-order schemes on 3D mixed-element meshes has been handled by the creation of a series of algorithms. These include the tetrahedralisation of the mesh, …
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Implementation and Verification of a Synthetic Eddy Method (SEM) in the Eagle3d Compressible Flow Solver
… with Weighted Essentially Non-Oscillatory (WENO) approximation to reduce numerical dissipation. SEM is a modern synthetic turbulence method able to reproduce an arbitrary Reynolds stresses specification on discretionary geometries while keeping computational costs low. The Large-Eddy …
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Modeling coupled physics and biology in ocean straits
… using the Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical model is verified against a Discontinuous-Galerkin (DG) numerical scheme on an unstructured grid. Several simulations of tidal flow are completed using bathymetry and flow magnitudes comparable to those found in the San …
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A Nondimensional Scaling Parameter for Predicting Pressure Wave Reflection in Stented Arteries
… of Weighted Essentially Non-Oscillatory (WENO) and Runge-Kutta methods. Over 100 cases were tested. Results showed that reasonable variations in these parameters could induce changes in reflection magnitude of up to ±50%. It was also discovered that the relationship between each of these …
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A Numerical Study of Supersonic Rectangular Jet Impingement and Applications to Cold Spray Technology
… with a tenth-order compact filter combined with WENO dissipation, almost everywhere except in a region around the bow shock where a fifth-order WENO scheme is used. A fourth-order low-storage Runge-Kutta scheme is used for time integration of gas dynamics equations simultaneously with solid …
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Relativistic neutron stars in general relativity and fourth order gravity
… coupled system of PDEs with a third order WENO scheme in space and an IMEX scheme in time. We obtained 18 frequencies from the Fast Fourier Transform (FFT) of the evolved perturbation equations, which were consistent with the frequencies of the neutron star's Sturm-Liouville problem. The …
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Leveraging numerical relativity formulations for perturbative analysis: applications to quasinormal modes in general relativity
… Using the Weighted Essentially Non-Oscillatory (WENO) finite difference method, we analyze three models derived from a polytropic equation of state: one stable, one marginally stable near the onset of instability, and one unstable. Our results consistent with those derived from standard methods, …
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Adjoint sensitivity analysis of the two-phase two-fluid model based on an approximate Riemann solver
… accurate in space and the solver using a WENO-type numerical flux is at least second-order accurate in space. For the adjoint tests, the results show that the adjoint sensitivity analysis framework works well for both steady-state problems and time-dependent problems. The adjoint …
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STRUCTURE-OPTIMIZED AND ORDER-PRESERVING METHODS FOR ADVECTION AND TIME STEPPING
… optimal limiter functions based on the class of WENO type methods. Limiter functions are applied to finite volume methods to avoid oscillations near discontinuities and sharp transitions for hyperbolic equations. Many limiter functions have been introduced in the literature.The general approach …
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Cluster Weather Vanes: Radio Galaxies as Indicators of Galaxy Cluster Dynamics
… 5th order Weighted Essentially Non-Oscillating (WENO) method. Appendices include other work on numerical methods used in the completion of this dissertation. We find that RG jets make excellent "weather-vanes" for understanding the dynamics of their surrounding media, and useful tools for …
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Unstructured Nodal Discontinuous Galerkin Method for Convection-Diffusion Equations Applied to Neutral Fluids and Plasmas
… discontinuous Galerkin method. TVB type and WENO type limiters are also studied to deal with numerical oscillations in regions with strong physical gradients in state variables. A high-order positivity-preserving limiter is also extended in this work to prevent negative densities and …
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Time-Domain Simulation of Sound Propagation in Frequency-Dependent Materials
… solver. The numerical method uses a high-order WENO scheme to accommodate the highly convective background flow at high Mach numbers. The study focuses on the acoustic field scaling laws scattered by the 2D and 3D vortices.
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Fast Sweeping Methods for Steady State Hyperbolic Conservation Problems and Numerical Applications for Shape Optimization and Computational Cell Biology
… with the numerical fluxes evaluated in WENO (Weighted Essentially Non-oscillatory) fashion, coupled with Gauss-Seidel iterations. In particular, we consider mainly the Lax-Friedrich numerical fluxes. Extensive numerical examples in both scalar and system test problems in one and two …
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Dielectric elastomer composites: analytical and numerical non-convex homogenization methods and applications
… as with numerical solutions generated via a new WENO finite-difference scheme developed specifically for this class of problems. With the object of scrutinizing recent experimental results, the specializations of the proposed solution to various cases wherein the filler particles are of poly- and …
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Speeding up high-order algorithms in computational fluid and kinetic dynamics: based on characteristics tracing and low-rank structures
… non-oscillatory scheme with adaptive order (WENO-AO); and the high-order temporal accuracy is achieved by explicit Runge-Kutta methods for convection equations and implicit-explicit (IMEX) Runge-Kutta methods for convection-diffusion equations. The algorithm extends to higher dimensions via …
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Computational Simulation of Detonation Waves and Model Reduction for Reacting Flows
Geometry is a crucial consideration in the design of detonation chambers of pulse detonation engines since it has a major impact on detonation ignition and operation efficiency. In this thesis, numerical simulations are used to study different geometrical configurations of detonation chambers and …
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