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Using ℓ1-Regularization for Shock Capturing in Discontinuous Galerkin Methods
Shock capturing is an essential part of numerical hyperbolic conservation laws. Most of the existing shock capturing methods are based on...
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Shock-Capturing Exponential Multigrid Methods for Steady Compressible Flows
AbstractIn this paper, a robust and efficient exponential multigrid framework is proposed for computing steady compressible flows. The algorithm...
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On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves
AbstractA comparative experimental accuracy study of three shock-capturing schemes (the second-order CABARET, third-order Rusanov, and fifth-order in...
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A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction–convection–diffusion equations
In this computational study, stabilized finite element solutions of convection-dominated stationary and linear reaction–convection–diffusion...
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A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods
In this paper, a new strategy for a sub-element-based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to...
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A p-Adaptive Discontinuous Galerkin Method with hp-Shock Capturing
In this work, we present a novel hybrid Discontinuous Galerkin scheme with hp-adaptivity capabilities for the compressible Euler equations. In smooth...
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On the Integral Convergence of Numerical Schemes Calculating Gas-Dynamic Shock Waves
AbstractA comparative analysis of the accuracy of shock-capturing schemes, such as the RBM (Rusanov–Burstein–Mirin), CWA (Compact high order Weak...
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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics
We study a temporal step size control of explicit Runge-Kutta (RK) methods for compressible computational fluid dynamics (CFD), including the...
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On the Accuracy of Discontinuous Galerkin Method Calculating Gas-Dynamic Shock Waves
AbstractThe results of a numerical calculation of gas-dynamic shock waves that arise in solving the Cauchy problem with smooth periodic initial data...
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Strong shock propagation for the finite-source circular blast in a confined domain
The circular explosion wave produced by the abrupt discharge of gas from a high-temperature heat source serves as a crucial model for addressing...
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Stabilizing Discontinuous Galerkin Methods Using Dafermos’ Entropy Rate Criterion: II—Systems of Conservation Laws and Entropy Inequality Predictors
A novel approach for the stabilization of the Discontinuous Galerkin method based on the Dafermos entropy rate crition is presented. First, estimates...
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Stabilizing Discontinuous Galerkin Methods Using Dafermos’ Entropy Rate Criterion: I—One-Dimensional Conservation Laws
A novel approach for the stabilization of the discontinuous Galerkin method based on the Dafermos entropy rate crition is presented. The approach is...
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A Class of Lagrangian–Eulerian Shock-Capturing Schemes for First-Order Hyperbolic Problems with Forcing Terms
In this work, we develop an improved shock-capturing and high-resolution Lagrangian–Eulerian method for hyperbolic systems and balance laws. This is...
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A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability
The HLLC approximate Riemann solver improves upon the HLL Riemann solver by resolving contact discontinuities. This is a particularly desirable...
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CWENO Finite-Volume Interface Capturing Schemes for Multicomponent Flows Using Unstructured Meshes
In this paper we extend the application of unstructured high-order finite-volume central-weighted essentially non-oscillatory (CWENO) schemes to...
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Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves
AbstractWe perform a comparative analysis of the accuracy of the weighted essentially nonoscillatory (WENO), compact high-order weak approximation...
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Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods
We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element...
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High Order Compact Central Spatial Discretization Under the Framework of Entropy Split Methods
Yee and Sjögreen (Comput Fluid 37:593–619, 2008) did a study on the performance between high order compact (Padé) spatial central finite...
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Combined Numerical Schemes
AbstractA survey of works concerning high-order accurate numerical methods designed for shock-capturing computations of discontinuous solutions to...
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New error estimates of Lagrange–Galerkin methods for the advection equation
We study in this paper new developments of the Lagrange–Galerkin method for the advection equation. In the first part of the article we present a new...
