Triangle based adaptive stencils for the solution of hyperbolic conservation laws
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Comparison of several spatial discretizations for the Navier-Stokes equations
Journal of Computational Physics
Mesh locking effects in the finite volume solution of 2-D anisotropic diffusion equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A generalized framework for high order anisotropic mesh adaptation
Computers and Structures
Accuracy preserving limiter for the high-order accurate solution of the Euler equations
Journal of Computational Physics
Hierarchical error estimates for finite volume approximation solution of elliptic equations
Applied Numerical Mathematics
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
High-order central ENO finite-volume scheme for ideal MHD
Journal of Computational Physics
WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
A Family of Finite Volume Schemes of Arbitrary Order on Rectangular Meshes
Journal of Scientific Computing
Hi-index | 31.51 |
High-order-accurate methods for viscous flow problems have the potential to reduce the computational effort required for a given level of solution accuracy. The state of the art in this area is more advanced for structured mesh methods and finite-element methods than for unstructured mesh finite-volume methods. In this paper, we present and analyze a new approach for high-order-accurate finite-volume discretization for diffusive fluxes that is based on the gradients computed during solution reconstruction. Our analysis results show that our schemes based on linear and cubic reconstruction can be reasonably expected to achieve second- and fourth-order accuracy in practice, respectively, while schemes based on quadratic reconstruction are expected to be only second-order accurate in practice. Numerical experiments show that in fact nominal accuracy is attained in all cases for two advection-diffusion problems, provided that curved boundaries are properly represented. To enforce boundary conditions on curved boundaries, we introduce a technique for constraining the least-squares reconstruction in boundary control volumes. Simply put, we require that the reconstructed solution satisfy the boundary condition exactly at all boundary flux integration points. Numerical experiments demonstrate the success of this approach, both in the reconstruction results and in simulation results.