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- Shu, Chi-Wang Stowell University Professor of Applied Mathematics

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- Shu, Chi-Wang Stowell University Professor of Applied Mathematics

- 2D semiconductor device simulations by WENO-Boltzmann schemes: Efficiency, boundary conditions and comparison to Monte Carlo methods
- A cell-centered Lagrangian scheme with the preservation of symmetry and conservation properties for compressible fluid flows in two-dimensional cylindrical geometry
- A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes
- A convergence study of a new partitioned fluid–structure interaction algorithm based on fictitious mass and damping
- A discontinuous Galerkin finite element method for directly solving the Hamilton–Jacobi equations
- A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations
- A family of time-staggered schemes for integrating hybrid DPD models for polymers: Algorithms and applications
- A finite element method to compute three-dimensional equilibrium configurations of fluid membranes: Optimal parameterization, variational formulation and applications
- A high order ENO conservative Lagrangian type scheme for the compressible Euler equations
- A high order moving boundary treatment for compressible inviscid flows
- A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws
- A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation
- A lattice Boltzmann model for coupled diffusion
- A new class of central compact schemes with spectral-like resolution I: Linear schemes
- A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes
- A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows
- A new method to impose no-slip boundary conditions in dissipative particle dynamics
- A numerical study for the performance of the Runge–Kutta discontinuous Galerkin method based on different numerical fluxes
- A phase field method for simulating morphological evolution of vesicles in electric fields
- A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains
- A second order discontinuous Galerkin fast sweeping method for Eikonal equations
- A sharp error estimate for the fast Gauss transform
- A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows
- A simple weighted essentially nonoscillatory limiter for Runge–Kutta discontinuous Galerkin methods
- A spectral viscosity method for correcting the long-term behavior of POD models
- A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway
- Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
- Adaptive wavelet collocation method on the shallow water model
- An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
- An effective bead–spring model for polymer simulation
- An interface treating technique for compressible multi-medium flow with Runge–Kutta discontinuous Galerkin method
- Anti-diffusive flux corrections for high order finite difference WENO schemes
- Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics
- Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow
- Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows
- Development of nonlinear weighted compact schemes with increasingly higher order accuracy
- Discontinuous Galerkin method based on non-polynomial approximation spaces
- Discontinuous Galerkin method for Krauseʼs consensus models and pressureless Euler equations
- Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
- Dispersive behaviour of high order finite element schemes for the one-way wave equation
- Dynamics of Self-Assembled Chaining in Magnetorheological Fluids
- Efficient implementation of high order inverse Lax–Wendroff boundary treatment for conservation laws
- Energy-conserving dissipative particle dynamics with temperature-dependent properties
- Equation-free/Galerkin-free POD-assisted computation of incompressible flows
- Exact PDF equations and closure approximations for advective-reactive transport
- Exponentially accurate spectral and spectral element methods for fractional ODEs
- Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations
- Flow in complex domains simulated by Dissipative Particle Dynamics driven by geometry-specific body-forces
- Force-coupling method for flows with ellipsoidal particles
- Fractional Adams–Bashforth/Moulton methods: An application to the fractional Keller–Segel chemotaxis system
- Fractional Sturm–Liouville eigen-problems: Theory and numerical approximation
- Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
- Gappy data: To Krig or not to Krig?
- Generalized fictitious methods for fluid–structure interactions: Analysis and simulations
- Hermite WENO schemes and their application as limiters for Runge–Kutta discontinuous Galerkin method: one-dimensional case
- Hermite WENO schemes for Hamilton–Jacobi equations
- Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells
- Hierarchical reconstruction for spectral volume method on unstructured grids
- High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
- High order conservative Lagrangian schemes with Lax–Wendroff type time discretization for the compressible Euler equations
- High order finite difference WENO schemes with the exact conservation property for the shallow water equations
- High order finite difference methods with subcell resolution for advection equations with stiff source terms
- High order residual distribution conservative finite difference WENO schemes for convection–diffusion steady state problems on non-smooth meshes
- High order residual distribution conservative finite difference WENO schemes for steady state problems on non-smooth meshes
- High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
- High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
- High-order well-balanced schemes and applications to non-equilibrium flow
- Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws
- Inverse Lax–Wendroff procedure for numerical boundary conditions of convection–diffusion equations
- Local discontinuous Galerkin methods for nonlinear Schrödinger equations
- Local discontinuous Galerkin methods for nonlinear dispersive equations
- Local discontinuous Galerkin methods for the Cahn–Hilliard type equations
- Local discontinuous Galerkin methods for the generalized Zakharov system
- Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
- Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection–diffusion equations on triangular meshes
- Modeling electrokinetic flows by the smoothed profile method
- Multi-element probabilistic collocation method in high dimensions
- Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition
- Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
- New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs
- Non-uniform order mixed FEM approximation: Implementation, post-processing, computable error bound and adaptivity
- Numerical methods for high-dimensional probability density function equations
- Numerical solution of the Stratonovich- and Ito–Euler equations: Application to the stochastic piston problem
- Numerical studies of the stochastic Korteweg-de Vries equation
- On maximum-principle-satisfying high order schemes for scalar conservation laws
- On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
- On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations
- Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media
- Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation
- Parallel multiscale simulations of a brain aneurysm
- Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws
- Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system
- Positivity-preserving Lagrangian scheme for multi-material compressible flow
- Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case
- Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part II: The two-dimensional case
- Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms
- Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
- Positivity-preserving method for high-order conservative schemes solving compressible Euler equations
- Predicting shock dynamics in the presence of uncertainties
- Quantification of sampling uncertainty for molecular dynamics simulation: Time-dependent diffusion coefficient in simple fluids
- Revisiting the redistancing problem using the Hopf–Lax formula
- Reweighted minimization method for stochastic elliptic differential equations
- Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations
- Runge–Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
- Runge–Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
- Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates
- Second-order approximations for variable order fractional derivatives: Algorithms and applications
- Smoothed profile method for particulate flows: Error analysis and simulations
- Special Issue on “Fractional PDEs: Theory, Numerics, and Applications”
- Spectral distributed Lagrange multiplier method: algorithm and benchmark tests
- Spurious behavior of shock-capturing methods by the fractional step approach: Problems containing stiff source terms and discontinuities
- Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier–Stokes equations
- Superconvergence and time evolution of discontinuous Galerkin finite element solutions
- The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
- Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics
- Towards stable coupling methods for high-order discretization of fluid–structure interaction: Algorithms and observations
- Triple-decker: Interfacing atomistic–mesoscopic–continuum flow regimes
- Uncertainty quantification in simulation science
- Velocity limit in DPD simulations of wall-bounded flows

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