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A new approach to prevent spurious behavior caused by conventionalshock-capturing schemes when solving stiff detonation waves problems isintroduced in the present work. Due to smearing of discontinuous solution bythe excessive numerical dissipation, conventional shock-capturing schemes havedifficulties to obtain the correct location of detonation front without enoughgrids resolution. To overcome the excessive numerical errors arounddiscontinuities by traditional discretized schemes used in non-reacting highspeed compressible flow, we introduce a new shock-capturing scheme in whichbesides linear function constructed by MUSCL (Monotone Upstream-centeredSchemes for Conservation Law) scheme, a step like THINC (Tangent of Hyperbolafor INterface Capturing) function is also employed as another candidate in thereconstruction process. The final reconstruction function is determined byboundary variation diminishing (BVD) algorithm by which numerical dissipationaround discontinuities can be reduced significantly. The new resultedshock-capturing scheme is named MUSCL-THINC-BVD. One- and two-dimensionalcomparative numerical tests about stiff detonation waves problems are conductedwith the 5th order WENO (Weighted Essentially Non-Oscillatory) andMUSCL-THINC-BVD scheme respectively, which show MUSCL-THINC-BVD scheme cancapture the correct position of detonation waves with improved resolution whileWENO scheme, in spite of higher order, produces spurious waves. Compared withother existing methods which involves extra treatments by accepting the smearedout discontinuities profiles, the current method obtain the correct but alsosharp detonation front by fundamentally reducing numerical dissipation errorsfrom shock-capturing schemes. Thus the proposed approach is an effective butsimple method to solve stiff detonation problems.

A new shock-capturing scheme for stiff detonation waves problems