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Positivity-Preserving Lax–Wendroff Discontinuous Galerkin Schemes for Quadrature-Based Moment-Closure Approximations of Kinetic Models
The quadrature-based method of moments (QMOM) offers a promising class of approximation techniques for reducing kinetic equations to fluid equations...
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High Order Compact Generalized Finite Difference Methods for Solving Inviscid Compressible Flows
This paper presents a novel generalized finite difference method that can achieve arbitrary order of accuracy on a compact stencil nodal set....
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On the Accuracy of a MUSCL-Type Scheme when Calculating Discontinuous Solutions
AbstractThe accuracy of the central difference Nessyahu-Tadmor (NT) scheme is studied when calculating shock waves propagating at a variable...
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Efficient Numerical Computations of Long-Wave Run-Up and Their Sensitivity to Grid Nesting
Computation of long-wave run-up has been of high interest in the fields of ocean sciences and geophysics—particularly for tsunami and river flood...
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A New S-M Limiter Entropy Stable Scheme Based on Moving Mesh Method for Ideal MHD and SWMHD Equations
For magnetohydrodynamics (MHD) equations, the existing entropy stable (ES) flux effectively eliminates the spurious oscillation, but it still has...
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Fifth-Order Hermite Targeted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws
We present a targeted essentially non-oscillatory (TENO) scheme based on Hermite polynomials for solving hyperbolic conservation laws. Hermite...
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Entropy–Based Methods for Uncertainty Quantification of Hyperbolic Conservation Laws
Using standard intrusive techniques when solving hyperbolic conservation laws with uncertainties can lead to oscillatory solutions as well as...
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Essentially Non-oscillatory Schemes Using the Entropy Rate Criterion
A newKlein, Simon-Christian definition of numerical fluxes for Finite-Volume schemes is given. These numerical flux functions directly use the...
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Effect of Adiabatic Index on Richtmyer-Meshkov Flows Induced by Strong Shocks
Richtmyer-Meshkov Instability (RMI) is an instability that develops at the interface between fluids of contrasting densities when impacted by a shock...
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Optimization of Artificial Viscosity in Production Codes Based on Gaussian Regression Surrogate Models
To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, the artificial viscosity has to be introduced to convert...
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A Characteristic-Featured Shock Wave Indicator for Conservation Laws Based on Training an Artificial Neuron
In this work, we use exact solutions of one-dimensional Burgers equation to train an artificial neuron as a shock wave detector. The expression of...
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Assessment of Upwind/Symmetric WENO Schemes for Direct Numerical Simulation of Screech Tone in Supersonic Jet
Screech tones are the high intensity shock-associated noise with discrete frequency in imperfectly supersonic jet. Accuracte numerical simulation of...
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Introduction
With the rapid development of electronic computers, numerical computation has become an important paradigm of scientific discovery as well as a...
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How to Design a Generic Accuracy-Enhancing Filter for Discontinuous Galerkin Methods
Higher order accuracy is one of the well-known beneficial properties of the discontinuous Galerkin (DG) method. Furthermore, many studies have...
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Combined DG Scheme That Maintains Increased Accuracy in Shock Wave Areas
AbstractA combined scheme for the discontinuous Galerkin (DG) method is proposed. This scheme monotonically localizes the fronts of shock waves and...
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A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor
A hybrid numerical flux scheme is proposed by adapting the carbuncle-free modified Harten-Lax-van Leer contact (HLLCM) scheme to smoothly revert to...
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Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Methods for KdV Type Equations
In this paper, several arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) methods are presented for Korteweg-de Vries (KdV) type equations...
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Revisit of dilation-based shock capturing for discontinuous Galerkin methods
The idea of using velocity dilation for shock capturing is revisited in this paper, combined with the discontinuous Galerkin method. The value of...
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A High Order Semi-implicit Scheme for Ideal Magnetohydrodynamics
In this work we design a novel semi-implicit finite volume solver for the equations of ideal magnetohydrodynamics (MHD). The nonlinear convective...
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An Efficient Low-Dissipation High-Order TENO Scheme for MHD Flows
In this paper, an efficient low-dissipation high-order TENO scheme is proposed for ideal MHD flows. For high computational efficiency, a...
