Results 61 to 70 of about 17,200,724 (197)
On the Application of the Discontinuous Galerkin Method to Turbomachinery Flows [PDF]
, 2012 This article describes the development of a Discontinuous Galerkin (DG) solver for 2D Euler flows with special emphasis on the implementation of robust and accurate boundary conditions for turbomachinary applications.
Ashcroft, Graham +2 more
core
High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation
Mathematics, 2018 The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and
He Yang
doaj +1 more source
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACT In this work, we present an extension of the semi‐discrete Lagrangian‐Eulerian numerical scheme for diffusive‐dispersive conservation law problems, including a jump discontinuous flux function. As in the one‐dimensional scalar hyperbolic case, the no‐flow curves also organize the geometry of the method.
Eduardo Abreu +2 more
wiley +1 more source
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations [PDF]
Journal of Scientific Computing, 2010 The authors discuss an \(hp\)-local discontinuous Galerkin (LDG) method for parabolic integro-differential equations. Preliminaries, basic results and the LDG method are presented. A priori error estimates for an extended mixed type Ritz-Volterra projection are discussed. Numerical examples are given to illustrate the predicted convergence rates.
Amiya Kumar Pani, Sangita Yadav
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Accurate and Efficient Data‐Driven Partitioned Scheme for Coupled Heterogeneous Numerical Models
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACT Heterogeneous numerical models (HNMs) combine conventional discretization modules such as finite elements with nonconventional data‐driven and reduced‐order modules. HNMs can improve computational efficiency and enable simulations of multi‐physics systems in which one or more constituent components lack first‐principles descriptions and must ...
Edward Huynh +3 more
wiley +1 more source
MathematicsIn this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs).
Xiaoxu Zhao +3 more
doaj +1 more source
Energies, 2014 The performance of modern heavy-duty gas turbines is greatly determined by the accurate numerical predictions of thermal loading on the hot-end components.
Zeng-Rong Hao +2 more
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Local Discontinuous Galerkin Method for the Backward Feynman-Kac Equation
Advances in Applied Mathematics and Mechanics34 ...
Dong Liu, Weihua Deng
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Rothe Time Discretization and Weak Solutions for a Cutoff Westervelt System
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACTWe study a fully implicit Rothe time discretization for a cutoff first‐order formulation of the Westervelt equation. The key ingredients are the enthalpy variable and the primitive mobility variable, which turn each nonlinear time step into a uniformly monotone elliptic problem and avoid higher‐order energy estimates and inverse inequalities ...
Marvin Fritz
wiley +1 more source
A Comparative Study of Low‐Dissipation Numerical Schemes for Hyperbolic Conservation Laws
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACT This work provides a comparative assessment of several low‐dissipation numerical schemes for hyperbolic conservation laws, highlighting their performance relative to the classical Harten‐Lax‐van Leer (HLL) schemes. The schemes under consideration include the classical Harten‐Lax‐van Leer‐Contact (HLLC), the recently proposed TV flux splitting,
Shaoshuai Chu, Michael Herty
wiley +1 more source