Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes

An explicit fourth-order orthogonal curvilinear staggered-grid FDTD method for Maxwell's equations

Journal of Computational Physics

High-order time-stable numerical boundary scheme for the temporally dependent Maxwell equations in two dimensions

Journal of Computational Physics

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

Journal of Scientific Computing

On the Conservation and Convergence to Weak Solutions of Global Schemes

Journal of Scientific Computing

High Order Finite Difference Approximations of Electromagnetic Wave Propagation Close to Material Discontinuities

Journal of Scientific Computing

Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows

Journal of Computational Physics

Finite volume methods, unstructured meshes and strict stability for hyperbolic problems

Applied Numerical Mathematics

Finite Volume Formulation of Compact Upwind and Central Schemes with Artificial Selective Damping

Journal of Scientific Computing

An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems

Journal of Computational Physics

Solving Schemes for Computational Magneto-Aerodynamics

Journal of Scientific Computing

High-order Compact Schemes for Nonlinear Dispersive Waves

Journal of Scientific Computing

A stable hybrid method for hyperbolic problems

Journal of Computational Physics

Short note: A high-order Padé ADI method for unsteady convection-diffusion equations

Journal of Computational Physics

On the order of accuracy for difference approximations of initial-boundary value problems

Journal of Computational Physics

A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows

Journal of Computational Physics

High-Order Compact ADI Methods for Parabolic Equations

Computers & Mathematics with Applications

Stable artificial dissipation operators for finite volume schemes on unstructured grids

Applied Numerical Mathematics

Grid stabilization of high-order one-sided differencing I: First-order hyperbolic systems

Journal of Computational Physics

Optimized High-Order Derivative and Dissipation Operators Satisfying Summation by Parts, and Applications in Three-dimensional Multi-block Evolutions

Journal of Scientific Computing

Boundary conditions for a divergence free velocity-pressure formulation of the Navier-Stokes equations

Journal of Computational Physics

A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions

Journal of Computational Physics

A stable and efficient hybrid scheme for viscous problems in complex geometries

Journal of Computational Physics

A class of energy stable, high-order finite-difference interface schemes suitable for adaptive mesh refinement of hyperbolic problems

Journal of Computational Physics

Stable and accurate schemes for the compressible Navier-Stokes equations

Journal of Computational Physics

A stable high-order finite difference scheme for the compressible Navier-Stokes equations

Journal of Computational Physics

A methodology for the development of discrete adjoint solvers using automatic differentiation tools

International Journal of Computational Fluid Dynamics

Stable and accurate wave-propagation in discontinuous media

Journal of Computational Physics

Large calculation of the flow over a hypersonic vehicle using a GPU

Journal of Computational Physics

Third-order Energy Stable WENO scheme

Journal of Computational Physics

On the outflow conditions for spectral solution of the viscous blunt-body problem

Journal of Computational Physics

High-Order Embedded Finite Difference Schemes for Initial Boundary Value Problems on Time Dependent Irregular Domains

Journal of Scientific Computing

Shock Capturing Artificial Dissipation for High-Order Finite Difference Schemes

Journal of Scientific Computing

Nondissipative and energy-stable high-order finite-difference interface schemes for 2-D patch-refined grids

Journal of Computational Physics

Numerical analysis of the Burgers' equation in the presence of uncertainty

Journal of Computational Physics

Stable Boundary Treatment for the Wave Equation on Second-Order Form

Journal of Scientific Computing

A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations

Journal of Computational Physics

Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators

Journal of Scientific Computing

Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods

SIAM Journal on Scientific Computing

Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes

Journal of Computational Physics

Interface procedures for finite difference approximations of the advection-diffusion equation

Journal of Computational and Applied Mathematics

Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations

SIAM Journal on Scientific Computing

Derivation of Strictly Stable High Order Difference Approximations for Variable-Coefficient PDE

Journal of Scientific Computing

Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions

Journal of Scientific Computing

Output error estimation for summation-by-parts finite-difference schemes

Journal of Computational Physics

A three-point sixth-order staggered combined compact difference scheme

Mathematical and Computer Modelling: An International Journal

Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

Journal of Computational Physics

Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

Journal of Scientific Computing

A Fourth Order Accurate Finite Difference Scheme for the Elastic Wave Equation in Second Order Formulation

Journal of Scientific Computing

Conservative integral form of the incompressible Navier-Stokes equations for a rapidly pitching airfoil

Journal of Computational Physics

Summation-by-parts operators and high-order quadrature

Journal of Computational and Applied Mathematics

Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions

Journal of Computational Physics

On the Accuracy and Stability of the Perfectly Matched Layer in Transient Waveguides

Journal of Scientific Computing

Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrödinger Equation

Journal of Scientific Computing

High Order Stable Finite Difference Methods for the Schrödinger Equation

Journal of Scientific Computing

Energy stable flux reconstruction schemes for advection-diffusion problems on triangles

Journal of Computational Physics

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

Journal of Computational Physics

Summation-by-parts in time

Journal of Computational Physics

Numerical investigation of the parabolic mixed derivative diffusion equation via Alternating Direction Implicit methods

Computers & Mathematics with Applications

Dual consistency and functional accuracy: a finite-difference perspective

Journal of Computational Physics

A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

Journal of Computational Physics

Duality based boundary conditions and dual consistent finite difference discretizations of the Navier-Stokes and Euler equations

Journal of Computational Physics

High-fidelity numerical solution of the time-dependent Dirac equation

Journal of Computational Physics

A Cartesian-based embedded geometry technique with adaptive high-order finite differences for compressible flow around complex geometries

Journal of Computational Physics

PDE-constrained optimization with error estimation and control

Journal of Computational Physics

Optimal diagonal-norm SBP operators

Journal of Computational Physics

A generalized framework for nodal first derivative summation-by-parts operators

Journal of Computational Physics