An adaptive projection method for the incompressible Euler equations

Conference · Wed Jun 09 04:00:00 EDT 1993

OSTI ID:6127044

Almgren, A S; Bell, J B; Howell, L H ^[1]; Colella, P ^[2]

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1. Lawrence Livermore National Lab., CA (United States)
2. California Univ., Berkeley, CA (United States)

In this paper we present a method for solving the time-dependent incompressible Euler equations on an adaptive grid. The method is based on a projection formulation in which we first solve convection equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the convection step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid flow. Our approach to adaptive refinement uses a nested hierarchy of grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which a coarse grid is advanced, fine grids are advanced multiple steps to reach the same time as the coarse grid and the grids are then synchronized. We will describe the integration algorithm in detail, with emphasis on the projection used to enforce the incompressibility constraint. Numerical examples are presented to demonstrate the convergence properties of the method and to illustrate the behavior of the method at the interface between coarse and fine grids. An additional example demonstrates the performance of the method on a more realistic problem.

• Research Organization: Lawrence Livermore National Lab., CA (United States)
• Sponsoring Organization: DOE; DOD; NSF; USDOE, Washington, DC (United States); Department of Defense, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-48; FG03-92ER25140
• OSTI ID: 6127044
• Report Number(s): UCRL-JC-113853; CONF-930714--2; ON: DE93016428; CNN: DMS-8919074; ACS-8958522; Agreement IACRO 93-817
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
FLUID FLOW
FLUID MECHANICS
IDEAL FLOW
INCOMPRESSIBLE FLOW
MATHEMATICAL LOGIC
MECHANICS
MESH GENERATION
NUMERICAL SOLUTION