Discretized Newton-relaxation solution of high resolution flux-difference split schemes

Strong Conservative Form of the Incompressible Navier–Stokes Equations in a Rotating Frame with a Solution Procedure

“…The numerical scheme used in this study is similar to that proposed by Pan and Chakravarthy [12] and is discussed in detail by Taylor [9] and Whitfield and Taylor [13]. An extensive discussion of the methodology applicable to twodimensional flows has been presented by Whitfield and Taylor [14].…”

“…Therefore, only the tools needed for constructing the inviscid fluxes are provided in Appendix A. The numerical method to be described has been presented in detail elsewhere [9,[12][13][14]. Only a brief description is given in the next section.…”

“…The approach taken in this work is to solve Eq. (A.1) implicitly using the discretized Newton-relaxation (DNR) scheme [13], where the fluxes at the cell faces are obtained using the Roe scheme [10] with higher order accuracy achieved using the MUSCL approach (van Leer [11]; Whitfield and Taylor [14]). Writing Eq.…”

A sliding interface method for unsteady unstructured flow simulations

“…The divergence term in brackets in the preceding equation is a temporal discretization of the change in the volume of the control volume and represents the geometric conservation law (GCL). A Newton iterative time evolution scheme is employed to advance the unsteady solution at each time step which linearizes the equations about a given time level and results in a linear system of equations that must be solved [27] …”

An Efficient Algorithm for Simulating Free-Surface Turbulent Flows around an Advancing Ship

“…The Roe matrix A is the Jacobian of the inviscid flux E expressed as (12) In Eq. ( 13 ) With introduction of the right-eigenvector R, the matrix A is expressed as (14) where IA is …”