in this work, a direct design approach for designing a surface shape (inverse design problem) has been developed, in which both the target surface pressure and the unknown nodal coordinates appear explicitly in the formulations. the final discretized form of the governing equations (unified formulation) can be used for both analysis and shape design problems. in this work, shape design problems...

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as “inadmissible”. For example, a cost functional which depends on the density, rather than on the pressure, is considered “inadmissible” for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian function...

two-dimensional euler equations have been solved on an unstructured grid. an upwind finite volume scheme, based on roes flux difference splitting method, is used to discretize the equations. using advancing front method, an initial delaunay triangulation has been made. the adaptation procedure involves mesh enrichment coarsening in regions of flow with high low gradients of flow properties, acc...

In this paper, we design stable and accurate numerical schemes for conservation laws with stiff source terms. A prime example and the main motivation for our study is the reactive Euler equations of gas dynamics. Furthermore, we consider widely studied scalar model equations. We device one-step IMEX (implicit-explicit) schemes for these equations that treats the convection terms explicitly and ...

This study aims at the theoretical development of a method of “four-dimensional analysis,” namcly the numerical variational analysis. The three basic types of variational formalism in the nurncrical variational analysis method are discussed. The basic formalisms are categorized into three areas: (1) “timewise localized” formalism, ( 2 ) formalism with strong constraint, and (3) formalism with w...

We present an extensible Julia-based solver for the Euler equations that uses a summationby-parts (SBP) discretization on unstructured triangular grids. While SBP operators have been used for tensor-product discretizations for some time, they have only recently been extended to simplices. Here we investigate the accuracy and stability properties of simplexbased SBP discretizations of the Euler ...